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है”ह”ह

IS 11717 (2000): Vocabulary on Vibration and Shock [MED 28:Mechanical Vibration and Shock]

lS 11717:2000ISO 2041:1990

( WR77@kwl

?-Ems

)

Indian Standard

VOCABULARY ON VIBRATION AND SHOCK

( First Revision)

ICS 17.160;01 .040.17

0 BIS 2000

BUREAU OF INDIAN STANDARDSMANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

May 2000 Price Group 11

JR--

Mechanical Vibration and Shock Sectional Committee, LM 04

NATIONAL FOREWORD

This Indian Standard ( First Revision) which is identical with 1S0 2041:1990 ‘Vibration and shock —Vocabulary’, issued by the International Organization for Standardization ( ISO ) was adopted by theBureau of Indian Standards on the recommendation of Mechanical Vibration and Shock SectionalCommittee and approval of the Light Mechanical Engineering Division Council.

This standard was first published in 1985. This first revision has been taken up to align with the latestversion of ISO 2041 which has been technically revised in 1990.

The text of ISO Standard has bden approved as suitable for publication as Indian Standard withoutdeviations. In the adopted standard, certain conventions are not identical to those used in IndianStandards. Attention is especially drawn to the following:

a) Wherever the words ‘International Standard’ appear referring to this standard, they should beread as’1 ndian Standard’.

b) Comma (, ) has been used as a decimal marker while in Indian Standards, the current practiceis to use a full point ( . ) as the decimal marker.

—

Indian Standard

VOCABULARY ON VIBRATION

( First Revision)

1S11717 :2000ISO 2041:1990

AND SHOCK

Scope

This International Standard defines terms inEnglish relating to vibration and shock. Analphabetical index is also provided.

1 General

1.1 displacement; relative displacement : Avector quantity that specifies the change of positionof a body, or particle, with respect to a referenceframe.

NOTES

1 The reference frame is usually a set of axes at a meanposition or a position of rest. In general, the displacementcan be representedby a rotationvector, a translationvector,or both,

2 A displacement is designated as relativedisplacementif it is measured with respect to a reference frame otherthan the primary reference frame designated in the givencase, The relative displacement between two points isthe vector difference between the displacements of thetwo points.

1.2 velocity; relative velocity : A vector thatspecifies the time-derivative of displacement.

NOTES

1 The reference frame is usually a set of axes at a meanposition or a position of rest. In general, the velocity canbe represented by a rotation vector, a translation vector,or both,

2 A velocity is designated as relative velocity if it ismeasured with respect to a reference frame other thanthe primary reference frame designated in a given case.The relative velocity between two points is the vectordifference between the velocities of the two points.

1.3 acceleration : A vector that specifies thetime-derivative of velocity.

NOTES

1 The reference frame is usually a set of axes at a meanposition or a position of rest. In general, the accelerationcan be represented bya rotationvector, a translationvector,or both,

2 An acceleration is designated as relative accelerationif it is measured with respect to a reference frame otherthan the inertial reference frame designated in a given case.The relative acceleration between two pointsis the vectordifference between the accelerations of the two points.

3 Variousself-explanatorymodifiers,suchas peak, average,and r.m,s. (root-mean-square), are often used. The time

1

intervalsover whichthe average or root-mean-squarevaluesare taken should be indicated or implied,

+. Acceleration maybe oscillatory, in which case simpleharmonic components can be defined by the accelerationamplitude (and frequency), or random, in which case ther.m.s. acceleration (and bandwidth and probability densitydistribution) can be used to define the probability that theacceleration will have values within any given range.Accelerationsof shorttime durationare definedas transientaccelerations. Non-oscillatory accelerations are definedas sustained accelerations, if of long duration, or asacceleration pulses, if of short duration,

1.4 acceleration of gravity, g: The accelerationproduced by the force of gravity at the surfaceof the Earth. It varies with the latitude and elevationof the point of observation.

NOTES

1 By international agreement, the value 980,665 m/s2(= 980,665 crn/s2= 386,089 in/s2= 32,1740 ft/s2)has beenchosen as the standard acceleration due to gravity (g).

2 Acceleration magnitude is frequently expressed as amultiple of g.

1.5 jerk: A vector that specifies the time-derivativeof acceleration.

1.6 inertial reference system; inertial referenceframe: A coordinate system in which the lawsof inertia (classical mechanics) are valid.

NOTE — Aninertial reference system signifiesa coordinatesystem which is fixed in space and, thus, not accelerating.

1.7 inertia force; inertial force :The reactionforce exerted by a mass when it is beingaccelerated.

1.8 oscillation :The variation, usually with time,of the magnitude of a quantity with respect to aspecified reference when the magnitude isalternately greater and smaller than some meanvalue.

1.9 sound :

(1) The sensation of hearing excitai by an acousticoscillation.

(2) Acoustic oscillation of such a character asto be capable of exciting the sensation of hearing.

(3) An oscillation in pressure, stress, particlevelocity, etc., in a medium with internal forces.

1S11717 :2000ISO 2041:1990

1.10 acoustics :The science and technology ofsound, including its production, transmission andeffects.

1.11 environment : The ag~regate, at a givenmoment, of all external conditions and influencesto which a system is subjected. [ See induced

environment (1. 12) and natwd environment (1.13).]

1.12 induced environment :Those conditionsexternal to a system generated as a result ofthe operation of the system.

1.13 natural environment : Those conditionsgenerated by the forces of nature and the effectsof which are experienced by a system when it isat rest as well as when it is in operation.

and that the principle of superposition can be applied tothe system.

1.22 mechanical system: An aggregate of mattercomprising a defined configuration of mass,stiffness and damping.

1.23 foundation : A structure that supports amechanical system. It maybe fixed in a specifiedreference frame or it may undergo a motion thatprovides excitation for the supported system.

1.24 seismic system : A system consisting ofa mass attached to a reference base by one ormore flexible elements. Damping is normallyincluded.

NOTES

1.14 preconditioning : The climatic and/or 1 Seismic systems are usually idealized as single degree-mechanical and/or electrical treatment wocedure of-freedom systems with viscous damping.

which may be specified for a particular system2 The natural frequencies of the mass as supported by

so that it attains a defined state. the flexible elements are relatively low for seismic systems

1.15 conditioning : The climatic and/orassociated with displacement or velocity pick-ups, andare relatively high for acceleration pick-ups, as compared

mechanical and/or electrical conditions to which with the range of frequencies to be measured.a system is subjected in order to determine theeffect of such conditions upon it. 3 When the natural frequency of the seismic system is

low relative to the frequency range of interest, the mass

1.16 excitation; stimulus : An external force of the seismic system may be considered to be at rest

(or other input) applied 10a system that causes over this range of frequencies.

the system to respond m some way. 1.25 equivalent system : A system that may

1.17 response (of a system) : A quantitative be substituted for another system for the purpose

expression of the output of the system. of analysis.

1.18 transmissibility: The non-dimensional ratioNOTE — Many typesof quivalence are commoninvibrationand shock technology:

of the response am~litude of a svstem in steadv-state forced vibratron to the exci~ation amplitud~. a) equivalent stiffness;

The ratio may be one of forces, displacements, b) equivalent damping;velocities or accelerations.

c) torsional system equivalent to a translational system;1.19 overshoot (undershoot) : If the output ofa system is changed from a steady value A to asteady value B by varying the input, such thatvalue B is greater (less) than A, then the responseis said to overshoot (undershoot) when themaximum (minimum) transient response exceeds(is less than) value B.

NOTE — The difference between the maximum (minimum)transient response and the value B is the value of theovershoot (undershoot).

1.20 system : An aggregate of the relevantand/or constituent parts of a device.

1.21 linear system : A system in which theresponse is proportional to the magnitude of theexcitation.

d) electricalor acousticalsystem equivalentto a mechanicalsystem, etc.

1.26 degrees of freedom: The number of degreesof freedom of a mechanical system is equal tothe minimum number of independent generalizedcoordinates required to define completely theconfiguration of the system at any instant of time.

1.27 single degree-of-freedom system : Asystem requiring but one coordinate to definecompletely its configuration at any instant.

1.28 multideg~f-freedom system: A systemfor which two or more coordinates are requiredto define completely the configuration of thesystem at any instant.

!

I

I

NOTE —This definitionimplies that the dynamic properties 1.29 continuous system; distributed system:of each element in the system can be represented by a A system having an infinite number of possibleset of linear differentialequationswithconstantcoefficients, independent configurations.

2

Is 11717:2000ISO 2041:1890

NOTE — The configuration of a continuous system is 1.36 neutral axis(of abeam insimpleflexure):specified by a function of a continuous spatial variable, or The trace of the neutral surface on any cross-variables, in contrast to a discrete or lumped parametersystem which requires only a finite number of coordinates

section of the beam.

to specify its configuration. 1.37 transfer function (of a system) : A

1.30 centre of gravity: That point through whichpasses the resultant of the weights of itscomponent particles for all orientations of thebody with respect to a gravitational field.

NOTE— If the field is uniform,thecentre ofgravitycoincideswith the cerrtre ofnrass (1,31 ).

1.31 centre of mass: The point associated witha body which has the property that an imaginaryparticle placed at this point with a mass equalto the mass of a given material system has afirst moment with respect to any plane equal tothe corresponding first moment of the system.

1.32 principal axes of inertia: For each set ofCartesian coordinates at a given point, the valuesof the six moments of inertia of a body lXtij (i, j =1, 2, 3) are in general unequal; for one suchcoordinate system, the products of inertia IXtij(i %j ) vanish. The values of IXtij (i = j ) for thisparticular coordinate system are called theprincipal moments of inertia and thecorresponding coordinate directions are calledthe principal axes of inertia.

NOTES

1 Izhj = /xixj dmfor i #j

Izuj= /(r2 -X12) dmfor i =j3

where r 2= ~ X,2 and xi and x, are Cartesian coordinates.1=1

2 if the point is the centre of mass of the body, the axesand momentsare called centralprincipalaxeeandcentralprincipal momenta of inertia.

3 In balancing, the term “principal inertia axis” is used todesignate the one central principal axis (of the three suchaxes) most nearly coincident withthe shaft axis of the rotorand is sometimes referred to as the “balance axis” or the“mass axis”.

1.33 stiffness, k: The ratio of change of force(or torque) to the corresponding change intranslational (or rotational) displacement of anelastic element.

mathematical relation between the output (orresponse) and the input (or excitation) of the system.

NOTE — It is usually given as a function of frequency,and is usually a complex function. [See response (1.17),transmissibility (1.1 8), transfer impedance (1.44) andfrequency response (B. 13).]

1.38 complex excitation : An excitation havingreal and imaginary parts.

NOTES

1 The concepts of complex excitations and responses ~were evolved historically in order to simplify calculations.The actual excitation and response are the real parts ofthe complex excitation and response. If the system islinear, the concept is valid because superposition holdsin such a situation.

2 This term should not be confused with excitation by acomplax vibration, or vibration of complex waveform.The use of the term “compiex vibration” in this sense isdeprecated,

1.39 complex response : The response of alinear system to a complex excitation. [See thenotes under complex excitation (1 .38).]

1.40 complex system parameter: A complexquantity that is, or is derived from, the ratio ofcomplex excitation to complex response.

NOTE — Electrical and mechanical impedances areexamples of complex system parameters.

1.41 impedance : The ratio of a harmonicexcitation of a system to its response (inconsistentunits), both of which are &mplex quantities andboth of whose arguments increase linearly withtime at the came rate. The term generally appliesonly to linear systems. [See mechanha/impeohnce(1.42).] - -

NOTES

1 The concept is extended to non-linear systems wherethe term incremental impedance is used to describe asimilar quantity,

2 The terms and definitions relating to impedance applyto systems undergoing sinusoidal vibrations oniy.

1.34 compliance :The reciprocal of stiffness. 1.42 mechanical impedance : At a point in amechanical system, the complex ratio of force

1.3S neutral surface (of abeam in simple flexure): to velocity where the force and velocity maybeThat surface in which there is no longitudinal taken at the same or different points in the samestress. system during simple harmonic motion.

NOTE — It should be stated whether or not the neutral NOTE — For the case of torsional mechanical impedance,surface is a result of the flexure alone, or whether it is a the words“force”and“velocity”shouldbe repiacedby“torque”result of the flexure and other superimposed loads. and “angular velocity”.

3

1S11717 :2000ISO 2041:1990

1.43 direct impedance; driving-point impe-dance : In a mechanical sense, the complexratio of the force to velocity taken at the samepoint in a mechanical system during simpleharmonic motion. [See the notes under impedance(1.41) and mechanica/impedance (1.42).]

1.44 transfer impedance: In a mechanical sense,the complex ratio of the force taken at one pointin a mechanical system to the velocity taken atanother point in the same system during simpleharmonic motions. [See the notes under impedance(1.41) and mechan~ca/impedance (1.42).]

1.45 free impedance :The ratio of the appliedexcitation force phasor to the resulting velocityphasor with all other connection points of thesystem free, i.e. having zero restraining forces.Free impedance is the arithmetic reciprocal of asingle element of the mobility matrix.

NOTES

1 Histroically,often no distinctionhas been made betweenblocked impedance and free impedance. Caution should,therefore, be exercised in interpreting published data.

2 While experimentally determined free impedances couldbeassembledintoa matrix,thismatrixwwld bequitedifferentfrom the blocked impedance matrix resulting frommathematicalmodellingof thestructureand,therefore,wouldnot conform to the requirements for using mechanicalimpedance in an overall theoretical analysis of the system.

1.46 loaded impedance: The loaded electricalimpedance of a transducer, or the loaded driving-point mechanical impedance of a structure, isthe impedance at the input when the output isconnected to its normal load or structure.

1.47 blocked impedance, Zu : The blockedelectrical impedance of a transducer, or the blockeddriving-point mechanical impedance of a structure,is the impedance at the input when the outputis connected to a load of infinite mechanicalimpedance.

NOTES

1 Blocked impedance is the frequency-response functionformed by the ratioof the phasor of the blockingor driving-

.

point force response at point i to the phasor of the appliedexcitation velocity at pointj, with all other measurementpoints on the structure “blocked”, i.e. constrained to havezero velocity. All forces and moments requiredto constrainfullyallpointsof intersetonthe structurehave tobe mea..uredin order to obtain a valied blocked impedance matri.:.

2 Any changes in the number of measurement points ortheir iocation will change the blocked impedances at allmeasurement points.

3 The primary usefulness of blocked impedance is inthe mathematical modeiling of a structure using lumpedmass, stiffness and damping elements or finite elementtechniques. When combining or comparing suchmathematical models with experimental mobility data, it isnecessary to convert the analytical blocked impedancematrix into a mobility matrix or vice versa.

1.48 frequency-response function : Thefrequency-dependent ratio of the motion-responsephasor to the phasor of the excitation force.

NOTES

1 Frequency-response functions are properties of lineardynamic systems which do not depend on the typeof excitation function. Excitation can be harmonic,random, or transient functions of time. The test resultsobtained with one type of excitation can thus be used forpredicting the response of the system to any other typeof excitation.

2 Lineartiy of the system is a condition which, in practice,will be met only approximately, depending on the type ofsystem and on the magnitude of the input, Care has to betaken to avoid non-lineareffects, particularlywhen applyingimpulse excitation. Structures which are known to be non-linear (for example certain riveted structures) should notbe tested with impulse excitation and great care is requiredwhen using random excitation for testing such structures.

3 Motion may be expressed in terms of either velocity,acceleration or displacement; the correspondingfrequency-response function designations are mobilityaccelerance and dynamic compliance or impedance,effective mass and dynamic stifhess, respectively (seetable 1).

1.49 frequency range of interest : Span, inHertz, from the lowest frequency to the highestfrequency at which, say, mobility data are to beobtained-in a given test series.

4

Is 11717:2000ISO 2041:1990

Table 1 — Equivalent definitions to be used for various kinds of measured outpuff!nput ratio

Term

Symbol

Unit

Boundary conditions

Seefigure

Comment

Term

Symbol

Unit

Boundary conditions

Comment

Term

Symbol

Unit

Boundary conditions

Comment

Motion expressed Motion expressed Motion expressedas displacement as velocity as acceleration

Dynamic compliance) Mobilityz) Accelerance3j.

xi/’F1 Yy= vi/~ a, /Fj

m/N m/(N,s) m/ (N.s2) = kg–’

Fk=o; k#j Fk=(); k#j Fk=O; k#j

3 1 2

Boundaryconditionsare easy to achieve experimentally.

Dynamic stiffness Blocked impedance Blocked effective mass

Fi/xj Zu= F/y Ftlal

N/m (N.s)/m (N.s2)/m = kg

Xk=o; k#J Vk=o; k#J” ak=o; k#j

Boundaryconditionsare very difficultor im~ssible to achieve experimentally.

Free dynamic stiffness Free impedance

N/m (N.s)/m

Fk=O; k#j Fk=O; k#j

Effective mass(free effective mass)

~/a,

(N,s2)/m = kg

Fk=O; k#j

Boundaryconditionsare easy to achieve, but resultsshall be used withgreat cautioninsystem modelling.

1) “Dynamiccompliance”is called “receptance”byseveral authors.

2) “Mobility”is sometimes called “mechanicaladmittance”.A typical plotis given in figure 1.

3) “Accelerance”has unfortunatelybeen called “inertance”in some publications.Inertance is not a standard term and isnot acceptable because it is in conflict with the common definition of acoustic inertance and also contrary to theimplicationcarried by the word“inertance”.

1.50 (mechanical) mobility, Y,j:The complex ratioof the velocity, taken at a point in a mechanicalsystem, to the force, taken at the same or anotherpoint inthe system, during simple harmonic motion.

NOTES

1 Mechanical mobility is the inverse of mechanicalimpedance.

2 Mobility is the frequency-response function formed bythe ratio of the velocity-response phasor at point i to the

excitationforce pha~orat pointj withall other measurementpointson the structureallowed to respondfreely withoutanyconstraints other than those constraints which representthe normalsuDoortof the structureinits intendedapplication.A typical plot‘isgiven infigure 1.

3 The velocity response can be either translational orrotational,and the excitationforce can be either a rectilinearforce or a moment.

4 If the velocity response measured is a translational oneand if the excitation force applied is a rectilinear one, theunits of the mobilityterm will be m/(N.s) in the SI system.

5

1S11717 :2000ISO 2041:1990

180900

-90-180

0

-20

-40

-60

-80

-100

.

—

70

1 I I I I I.- --10 20 50 100 200

Frequency,Hz

Figure 1 — Mobility plot

500 1000 2 000

I

20 I 0,1kq

0

-20

rz7” “

I

I.

I / I I I I I10 20 50 100 200 500 1000 2000

Frequency,Hz

Figure 2 — Accelerance magnitude plot corresponding to the mobility graph plotted in figure 1

6

1S11717 :2000ISO 2041:1990

104 N/m i I

105N/m

-106N/m I

_ 10eN/mStiffness

I 1 II

10 20 50 100 200 500 1000 2000Frequency,Hz

Figure3— Dynamic compliance magnitude plot corresponding to the mobility graphplotted in

1.51 direct (mechanical) mobility; driving-point(mechanical) mobility, ~j :The complex ratio ofvelocity and force taken at the same point in amechanical system during simple harmonic motion.

NOTES

1 Driving-pointmobilityis the frequency-response functionformed by the ratio, in metres per newton second, of thevelocity-response phasor at point j to the excitation forcephasorappliedat the same pointwithall other measurementpointson the structureallowed to respondfreely withoutanyconstraints other than those constraints which representthe normalsupportof the structurein itsintendedapplication.

2 The term “point”cfesignatasa locationand a direction,Theterm “coordinate”has also been usadwiththesame meaningas “point”.

1.52 frequency-averaged mobility magnitude:The r.m.s. vaiue of the ratio, in metres per newtonsecond, of the magnitude of the velocity responseat point i to the magnitude of the exciting force atthe same point, averaged over specified frequencybands.

1.53transfer (mechanical) mobiiity: The compiexratio of the velocity, taken at one point in amechanical system, to the force, taken at another

7

figure 1

point in the same system, during simple harmonicmotion.

NOTE —Transfer mobilityis thefraquency-responsefunctionformed by the ratio, in metres per newton second, of thevelocity-response phasor at point i to the excitation forcephasorappliedat pointjwith ail pointsotherthanjallowed torespond freely without any constraints other than thoseconstraints which represent the normal support of thestructure in its intendad application.

1.54 dynamic stiffnes% dynamic eiasticconstant; dynamic spring constant, k.:

(1) The ratio of change of force to change ofdisplacement under dynamic conditions.

(2) The compiex ratio of force to displacementduring simple harmonic motion.

NOTES

1 The dynamic stiffness may be dependent upon strain(amplitude and/or spectrum), strain-rate, temperature orother conditions,

2 The dynamic stiffndss, k ., of a linear translationalsingle-degree-of-freedom system characterized by theequation.

\

1S11717:2000ISO 2041:1990

where F = FOe’”t,is equal to

k.=$, =k–mw~+iaOc

In these equations,

m is the mass;

x is the displacement;

1 is the time;

c is the linear (viscous) damping coefficient;

k is the elastic (spring) constant;

F, is the force amplitude;

e is the base’of natural logarithms;

i= m

m is the angular frequency;

@ois the undamped natural frequency;

is the displacement amplitude,Xo

1.55 apparent mass; effective mass : Thecomplex ratio of force to acceleration during simple

harmonic motion.

NOTE — The ratio of force to acceleration, when theacceleration is given in terms of g, is sometimes calledeffective weight or effective load.

1.56 spectrum : A description of a quantity as afunction of frequency or wavelength.

NOTE — The term “specturm” may be used to signify acontinuous range of components, usually tide in extent,which have some common characteristics, for exampleaudio-frequency spectrum.

1.57 level (of a quantity) : the logarithm of theratio of the quantity to a reference of the samekind. The base of the logarithm, the referencequantity and the kind of level shall be specified.

NOTES

1 Examples of kinds of levels in common use are electric-power level, sound-pressure level, voltage-squared level.

2 The level as defined in this international Standard ismeasured in unitsof the logarithmof a reference ratiothat isequal to the base of the logarithms,

3 The definitionis expressed symbolically as

where

L is the level of the kind determined by the kind ofquantity under consideration, measured in units ofIogf;

r is the base of the logarithmsand the reference ratio;

q is the quantity under consideration;

4

5

qO is the reference quantity of the same kind,

A difference in the levels of two like quantities q, andqz k described by the same formula because, by therulesof logarithms,the referencequantityis automaticallydivided out as follows:

‘ogr(%)-’ogr(+ogIn vibrationterrnlnol~y, the term “level”may sometimesbe usedto denoteamplitude, average value, root-mean-square value, or ratios of these values. These uses aredeprecated.

1.58 bet : A unit of level when the base of thelogarithm is 10. Use of the bel is restricted to levelsof quantities proportional to power. [See the notesunder /eve/(l .57) and decibe/(1 .59).]

1.59 decibel (dB): One tentn of a bel.

NOTES

1 The magnitude of a level in decibels is ten times thelogarithmto the base 10 of the ratioof power-like quantities,i.e.

‘,=’010910(5) ‘2010’0(:)

2 Examples of quantities that qualify as power-likequantities are sound-pressure squared, particle-velocitysquared, sound intensity, sound-energy density, voltagesquared. Thus the bel is a unit of sound-pressure-squaredlevel; it is common practice, however, to shorten this tosound-pressure level because ordinarily no ambiguityresults from so doing.

2 Vibration

2.1 vibration : The variation with time of the

magnitude of a quantity which is descriptive of themotion or position of a mechanical system, whenthe magnitude is alternately greater and smallerthan some average value or reference. [See

osci//ation (1.8).]

2.2 periodic vibration : A periodic quantity thevalues of which recur for certain equal incrementsof the independent “variable.

NOTES

1 A periodicquantity,y, which is a function of time, t, can ,be expressed as

y=~(t)=/(t*n T)

where

n is a whole numbec

r is a constant;

t is an independentvariable,

2 Aquaei-periodicvibration is a vibrationwhichdeviatesonly slightlyfrom aperiodic vibration.

8

1S11717 :2000

2.3 simple harmonic vibration; sinusoidalvibration: Aperiodic vibration that is a sinusoidalfunction of the independent variable. Thus

y= Asin(Ot+@)

where

Y is the simple harmonic vibration;

A is the amplitude;

o is the angular frequency;

t is the independent variable;

@ is the phase angle of the vibration.

NOTES

1 The maximum value of the simple harmonic vibration istheamplituded.

2 A periodic vibration consisting of the sum of more thanone sinusoid,each having a frequency whichis a multipleofthe fundamentalfrequency,isoften referredto as a complexvibration or multi-sinusoidal vibration. The use of theterm “complexvibration”in this context is deprecated.

3 A quasi-sinusoidal vibration has the appearance of thesinusoid,butvaries relatively slowly infrequency and/or inamplitude,

2.4 random vibration: A vibration the magnitudeof which cannot be precisely predcted for any giveninstant of time. [See random noise (2.7).]

NOTE — The probability that the magnitude of a randomvibration is within a given range can be specified by aprobabilitydistrib~tionfunction.

2.5 non-stationary vibration: A random vibrationthat is not stationary.

2.6 noise:

(1) Any disagreeable or undesired sound.

(2) Sound, generally of a random nature, thespectrum of which does not exhibit clearly definedfrequency components.

NOTE — By extension of the above definitions, noise mayconsist of electrical oscillations of an undesired or randomnature. If ambiguity exists as to the nature of the noise, aterm such as acoustic noise or electrical noise shouldbeused.

2.7 random noise : A noise the magnitude ofwhich cannot be precisely predicted for any giveninstant of time. [See random vibration (2.4) andthe accompanying note.]

2.8 Gaussian random noise : A random noisewhose instantaneous magnitudes have a Gaussiandistribution. [See Gaussian distribution (A.32).]

2.9 white noise; white random vibration: Whitenoise has equal energy for any frequency band of

ISO 2041:1990

constant width (or per unit bandwidth) over thespectrum of interest.

NOTE — White random vibration has a constant mean-square acceleration spectral density over the frequencyspectrum of interest. [See power spectra/density (5.1).]

2.10 pink noise; pink tttndom vibration: A noise

which has a constant energy within a bandwidthproportional to the centre frequency of the band.

NOTE —The energy spectrum of pink noise as determinedby an octave bandwidth (or any fractional part of an octavebandwidth)filter will have a constant value.

2.11 narrow-band random vibration: Randomvibration having its frequency components within

a narrow band only [See random vibration (2.4).]

NOTES

1 The defining of what is meant by “narrow”is a relativematter depending upon the problem involved. It is usuallyequal to or less than 1/3 octave.

2 The waveformof a narrow-bandrandomvibrationhas theappearance of a sine wave the amplitudeand phaseof whichvary in an unpredictable manner.

2.12 broad-band random vibration : Randomvibration having its frequency componentsdistributed over a broad frequency band. [Seerandom vibration (2.4).]

NOTE — The definition of what is meant by “broad”is arelative matter depending upon the problem involved. N isusually one octave or greater.

2.13 dominant frequency: A frequency at whicha maximum value occurs is a spectral densitycurve.

2.14 steady-state vibration : A steady-statevibration exists if the vibration is a continuingperiodic vibration.

2.15 transient vibration :The vibratory motion ofa system other than steady-state or random.

NOTE —This term is basically associated with mechanicalshock (3.1).

2.16 forced vibration [oscillation]: The steady-state vibration [oscillation] caused by a steady-state excitation.

NOTES

1 The vibration(forIinearsystems) has the same frequenciesas the excitation.

2 Transientvibrations [oscillations] are not considered.

2.17 free vibration; free oscillation : Vibrationthat occurs after the removal of excitation orrestraint.

9

Is 11717:2000ISO 2041:1990

NOTE — The system vibrates at natural frequencies of thesystem,

2.18 self-induced vibration; self-excitedvibration : Vibration of a mechanical system

resulting from conversion, within the system, ofnon-oscillatory energy to oscillatory excitation.

2.19 ambient vibration : The all-encompassingvibration associated with a given environment,

being usually a composite of vibration from manysources near and far.

2.20 extraneous vibration : The total vibrationother than the vibration of principal interest.

NOTE — Ambientvibration contributesto the magnitude ofextraneous vibration.

2.21 aperiodic motion : A vibration that is not

periodic.

2.22 cycle (noun) :The complete range of statesor values through which a periodic phenomenon orfunction passes before repeating itself identically.

[ See eye/e (verb) (2.101 ).]

2.23 fundamental period; period: The smallest

increment of the independent variable of a periodic

quantity for which the function repeats itself. [Seeperiodic vibration (2.2).]

NOTE — If no ambiguity is likely, the fundamental period iscalled the period,

2.24 (cyclic) frequency : The reciprocal of thefundamental period.

NOTE — The unit of frequency is the hertz (Hz), whichcorresponds to one cycle per second.

2.25 fundamental frequency:

(1) Of a periodic quantity, the reciprocal of thefundamental period.

(2) Of an oscillating system, the lowest naturalfrequency.The normal mode of vibration associatedwith this frequency is known as the fundamentalmode.

2.26 harmonic (of aperiodic quantity): A sinusoiathe frequency of which is an integral multiple ofthe fundamental frequency.

NOTES

1 The term overtone has frequently been used in place ofharmonic,the# harmonicbeingcalledthe (n -1 )h overtone.

2 In English,the firstovertone and the secondharmonicareeach twice the frequency of the fundamental. In French, thedistinctionbetween harmonic and overtone does not exist,and the second harmonic is twice the frequency of thefundamental. The term “overtone” is now deprecated toreduce ambiguity in the numbering of the components of aperiodicqgantity,

2.27 subharmonic : A sinusoidal quantity theperiod of which is an integral submultiple of thefundamental period of the quantity to which it isrelated.

2.28 beats : Periodic variations in the amplitudeof an oscillation resulting from the combination oftwo oscillations of slightly different frequencies.The beats occur at the difference frequency.

2.29 beat frequency: The absolute value of thedifference infrequency of two oscillations of slightlydifferent frequencies.

2.30 angular frequency; circular frequency :The product of the frequency of a sinusoidal quantityand the factor 2x.

NOTE —The unitof angular f;equency is the radianper unitof time.

2.31 phase ang!e; phase (of a sinusoidalvibration) :The fractional part of a period through

which a sinusoidal vibtation has advanced asmeasured from a value of the independent variableas a reference.

2.32 phase difference; phase angle difference:Between two periodic vibrations of the samefrequency, the difference between their respective

phases or, in the case of sinusoidal vibrations,

between their phase angles measured from thesame origin.

2.33 amplitude : The maximum value of a

sinusoidal vibration.

NOTES

1 This is sometimes called vector amplitude to distinguishit from other senses of the term “amplitude”, and it issometimes called sing!e amplitude, or peak amplitude,todistinguishit fromdoubleamplitude, which fora simpleharmonic vibration is the same as the total excursion (adisplacement concept) or peak-to-peak value. The use ofthe terms “double amplitude” and “single amplitude” isdeprecated.

2 In the vibrationtheory,the use of “amplitude”,forpurposesother than to describe the maximum value of a sinusoid, isdeprecated.

2.34 peak value; peak magnitude; positive(negative) peak value: The maximum value of avibration during a given interval. [ See alsornaxirnurn vakfe (2.40). ]

NOTE — A peak value vibration is usually taken as themaximum deviation of that vibration from the mean value,A positivepeak vaiue is the maximum positivedeviationanda negative peak value is the maximum negative deviation.

2.35 peak-to-peak value (of a vibration) : Thealgebraic difference between the extreme values

of the vibration.

10

1S11717 :2000ISO 2041:1990

2.36 excursion; total excursion (of a vibration): NOTE — If the nature of the antinode is not apparent, an

The peak-to-peak displacement. appropriate modifier should be used, for exampledisplacement antinode, pressure, antinode, etc.

2.37 crest factor (of a vibration); peak-to-r.m.s.ratio : The ratio of the peak value to the r.m.s. 2,48 mode of vibration: In a system undergoing

value. vibration, a mode of vibration designates thecharacteristic pattern of nodes and antinodes

NOTE —Thevalue of the crest factor of a sine wave is ~~. assumed by the system in which the motion of

2.38 form factor (of a vibration): The ratio of the every particle, for a-particular frequency, is simple

r.m.s. value to the mean value for one-half cycle harmonic (for linear systems) or has corresponding

between two successive zero crossings. decay patterns.

NOTE —The form factor for a sinusoid is 7d2 ~ = 1,111. NOTE — Two or more modes may exist concurrently in amulti-degree-of-freedom system.

2.39 instantaneous value; value: The value of avariable quantity at a given instant. 2.49 natural mode of vibration : A mode of

vibration assumed by a system when vibrating2.40 maximum value : The value of a function freely.when any small change inthe independent variablecauses a decrease in the value of the function. NOTES

2.41 maximax : The maximum value that is of 1 If the system has zero damping, the natural modes are

greatest magnitude when a function contains morethe same as the normal modes. [see norms/mode (2.55).]

than one maximum value within a given interval ofthe independent variable.

2.42 vibration severity : A generic term thatdesignates a value, or set of values, such as amaximum value, average or r.m.s. value, or otherparameter that is descriptive of the vibration. Itmay refer to instantaneous values or to averagevalues.

NOTES

1 The vibration severity of a machine is defined by themaximum r.m.s. value of the vibration velocities measuredat significant points of a machine, such as bearings ormountings.

2 The duration of a vibration is sometimes included as aparameter descriptive of vibration severity. This usage isdeprecated.

2.43 elliptical vibration: A vibration in which thelocus of a vibrating point is elliptical in form.

2.44 rectilinear vibration; linear vibration : Avibration in which the locus of a vibration point is astraight line.

2.45 circular vibration : A vibration in which thelocus of a vibrating point is circular in form. This isa special case of elliptical vibration.

2 A natural mode of vibration exists for each degree offreedom of the system.

2.50 fundamental natural mode of vibration :The mode of vibration of a system having the lowestnatural frequency. [see hmdamenkd frequency(2.25).]

2.51 mode shape : The mode shape of a givenmode of vibration of a mechanical system is givenby the maximum change in position, usuallynormalized to a specified deflection magnitude ata specified point, of its neutral surface (or neutralaxis) from its mean value. The mean value is themean for the given mode of vibration only.

2.52 modal numbers: When the normal modesof a system are identified by sets of integers, theseintegers are called modal numbers.

2.53 coupled modes : Modes of vibration thatare not independent but which influence one anotherbecause of energy transfer from one mode toanother.

2.54 uncoupled modes: Modes of vibration thatcan exist in a system concurrently with andindependently of other modes, no energy beingtransferred from one mode to another.

2.46 node : A point, line or surface in a standing2.55 normal mode : A natural mode of an

wave where some characteristic of the wave fieldhas essentially zero amplitude.

undamped mechanical system.

NOTE — If the nature of the node is not apparent, anNOTES

appropriate modifier should be used, for exampledisplacement node, pressure node, etc.

1 The motionof a system consists of the summation of thecontributionof each of the participating normal modes.

2.47 antinode; loop: A point, line or surface in a 2 The terms natural mode, characteristic mode andstanding wave where some characteristic Uf the eigen mode are synonymous with normal mode forwave field has a maximum value. undamped systems.

11

1S11717 :2000ISO 2041:1990

2.56 wave : A modification of the physical stateof a medium, which is propagated through themedium by virtue of the physical characteristicsof the medium.

NOTE — At any point in the medium the quantityserving asa measure of the disturbances is a function of time and atany instant the quantity is a functionof position.

2,57 wave train: A succession of a limited numberof waves, usually nearly periodic, traveling at thesame (or nearly the same) velocity.

2.58 wavelength ( of a periodic wave ) : Thedistance measured perpendicular to the wave frontin the direction of propagation, between twosuccessive points on the wave, which areseparated by one period.

2.59 compressional wave : A wave ofcompressive or tensile stresses propagated in anelastic medium.

NOTE — A compressional wave is normally a longitudinalwave, [See /orrgitudin8/ wave (2.60).]

2.60 longitudinal wave : A wave in which thedirection of displacement caused by the wavemotion is parallel to the direction of propagation.

2.61 shear wave : A wave of shear stressespropagated in an elastic medium.

NOTES

1 A shear wave is normally a transverse wave. [Seetransverse wave (2,62).]

2 A shear wave causes no changes in volume.

2.62 transverse wave: A wave of displacementof elements of the medium propagatedperpendicular to the wave front.

2.63 wave front:

(1) Of a progressive wave in space, the continuoussurface which is a locus of points where the phaseis the same at a given instant.

(2) Of a progressive surface wave, the continuousline which is a locus of points where the phase isthe same at a given instant.

2.64 plane wave : A wave in which the wavefronts are parallel planes.

2.65 spherical wave: A wave in which the wavefronts are concentric spheres,

2.66 standing wave : A periodic wave having afixed amplitude distribution in space, i.e. the result

of interference of progressive waves of the samefrequency and kind.

NOTES

1 A standing wave can be considered to be the result ofsuperpositionof opposing progressive waves of the samefrequency and kind.

2 Standingwaves are characterizedby nodesand antinodesthat are fixed in position.

2.67 audio frequency : Any frequency of anormally audible sound wave.

NOTE —Audio frequenciesgenerally lie between 20 HZand20000 Hz.

2.68 ultrasonic frequency; ultrasonic : afrequency lying above the audio frequency range.

NOTE —The term “ultrasonic”may be used as a modifiertoindicate a device intended to operate in association withultrasonicvibrations.

2.69 infrasonic frequency; infrasonic : Afrequency lying below the audio frequency range.

NOTE —The term “infrasonic”may be used as a modifiertoindicate a device intended to operate in association withinfrasonicvibrations.

2.70 reverberation : The sound that persists inan enclosed space, as a resutl of repeated reflectionor scattering, after the source of the sound hasstopped.

2.71 echo : A wave that has been reflected orreturned with sufficient magnitude and delay tobe detected as a wave distinct from that directlytransmitted and distinguishable as a repetitionof it.

2.72 resonance: Resonance of a system inforcedoscillation exists when any change, however small,in the frequency of excitation causes a decreasein a response of the system.

2.73 resonance frequency: A frequency at whichresonance exists.

NOTES

1 Resonance frequencies may depend uponthe measuredvariables, for example velocity resonance may occur at adifferent frequency from that of displacement resonance.(See table 2.)

2 In case of possibleconfusion,the type of resonance shallbe indicated,forexamplevelocityresonancefrequency.(Seetable 2).

2.74 antiresonance: Antiresonance of a systemin forced oscillation exists at a point when any

12

Is 11717:2000ISO 2041:1990

Table 2 — Resonance rel~lons

Characteristic Displacement Velocity Damped naturalresonance resonance frequency

%quency, HZkm k~ km

Amplitudeof displacementA A

r

k C’r

kc—

c —.— m cti4m’

Amplitudeof velocity A

4+

2 A

4mk-2c27 Cti

Phase of displacement withreference to applied force tan-’ & c’ ‘2 $ tan-i F

NOTES

1 In the case of a linear single degree-of-freedom system, the motionof whichcan be described by the equation

&m—z+c+

dr~+kx=ACosa)t

where

x is a displacement

o is the angular frequeacfi

m, c and k are constants;

the characteristics of the different kindsof resonance in terms of the constantsof the above equationareas given in thetable.

2 Forvalues of cwhich are small compared with &k there is littledifference between the three cases. The frequencyat velocity resonance is equal to the undamped natural frequency of the system, Other symbols are employed forelectrical resonance.

change, however small, in the frequencv of foundation to which the equipment is attached wereexcitation causes an increase in a response atthis point.

2.75 antiresonance frequency: A frequency atwhich antiresonance occurs.

NOTES

1 Aptiresonance frequencies may depend upon themeasuredvariable, for example velocityantiresonancemaycecur at a different frequency from that of displacementantiresonance.

rigid and of infinite rnass~ “

NOTE — The equation given in tabte 2 and the naturalfrequenciesshownareforfixed-baseconditions.

2.77 critical speed : A characteristic speed atwhich resonances of a system are excited.

NOTES

1 Critical speed of a rotating system is a speed of therotatingsystem that correspondsto a resonance frequency(it may also include multiples and submultiple of the

2 In cases of possible confusion, the type of resonance frequency) of the system, for example speed in

antiresonance shall be indicated, for example velocity revolutionsper unittime equals the resonance frequency in

antiresonance frequency. cycles per unittime.

2.76 fixed-base natural frequency : A natural2 Wherethereare severalrotatingsystems,therewillbe

frequency that a system would have if theseveralcorrespondingsetsofcriticalspeeds,one for eachmode of the overall system,

13

Is 11717:2000ISO2041:1990

2.78 subharmonic response; subharmonicresonance response: A response of a mechanicalsystem exhibiting some of the characteristics ofresonance at a frequency having a period which isan integral multiple of the period of excitation.

2.79 damping : The dissipation of energy withtime or distance.

NOTE — In the context of vibration and shock, damping isthe progressive reductionof the amplitude with time.

2.80 undamped natural frequency (of amechanical system) : A frequency of free vibrationresulting from only elastic and inertial forces ofthe system.

NOTE — For the equation of motion given in table 2, theundamped natural frequency is (1/2 n) ~k/m Hz,

2.81 damped natural frequency: The frequencyof free vibration of a damped linear system. (Seetable 2.)

2.82 viscous damping; linear viscousdamping : The dissipation of energy that occurswhen an element or a part of a vibration system isresisted by a force the magnitude of which isproportional to the velocity of the element and thedirection of which is opposite to the direction ofthe velocity.

2.83 equivalent viscous damping : A value oflinear viscous damping, assumed for the purposeof analysis of a vibratory motion, such that thedissipation of energy per cycle at resonance is thesame for the assumed as well as for the actualdamping force.

2.84 linear viscous damping coefficient;viscous damping coefficient: For linear viscousdamping, the ratio of damping force to velocity.[See //near viscous cfarnping (2.82).]

2.85 critical damping; critical viscousdamping: For a single degree-of-freedom system,

the amount of viscous damping which correspondsto the limiting condition between an oscillatory anda non-oscillatory transient state of free vibration.

NOTE — The critical Iinearviscous dampingcoefficient, CC,is equal to

Cc = 2 ~imk = 2m64

for the single degree-of-freedom system representedby the equation given in table 2, where COOis theundampednaturalfrequency(angular),[See undampednafura/ frequency (2.80).]

2.86 damping ratio; fraction of criticaldamping : For a system with linear viscousdamping, the ratio of the actual damping coefficientto the critical damping coefficient. [See hear

viscous damping coefficient (2.84) and criticaldamping (2.85).]

NOTE — The fraction of critical damping may also beexpressed in terms of percent of critical damping.

2.87 logarithmic decrement : The naturallogarithm of the ratio of any two successiveamplitudes of like sign in the decay of a single-frequency oscillation.

2.88 non-linear damping : Phenomenonassociated with the energy loss of a systemwhereby the motion of the system cannot becharacterized by a linear differential, integral orintegro-differential equation with constantcoefficients.

2.89 Q; Q factor: A quantity which is a measure ofthe sharpness of resonance, or frequencyselectivity, of a resonant oscillatory system havinga single degree of freedom, either mechanical orelectrical.

NOTE —The quantityQ is equal to one-half the reciprocalofthe damping ratio:

Q= L2 Cfcc

2.90 vibration generator; vibration machine: Amachine that is specifically designed for and is

capable of generating vibrations and of impartingthese vibrations to other structures or devices.

NOTE — Equipmentto be testfxi may be attached to a tableon the generator or the generator may be used to exciteequipment by means of studs without the use of a table.

2.91 vibration generator system: The vibrationgenerator and associatai equipment necessary forits operation.

2.92 electrodynamics vibration generator;electrodynamics vibration machine: A vibrationgenerator which derives its vibratory force from theinteraction of a magnetic field of constant value,and a coil of wire contained in it which is excitedby a suitable alternating current.

NOTE —The moving element ofan elactrodynamicvibrationgenerator includes the vibration table, the moving coil, andall the parts of the generator that are intended to participateinthe vibration.

2.93 electromagnetic vibration generator : Avibration generator which derives its vibratory force

from the interaction of electromagnets and magnetic

materials.

2.94 mechanical direct-drive vibration

generator; direct-drive vibration generator: Avibration machine in which the vibration table is

forced, by a positive linkage, to undergo a

14

displacement amplitude of vibration that remainsessentially constant regardless of the load orfrequency of operation.

2.95 hydraulic vibration generator: A vibrationgenerator which derives its vibratory force from theapplication of a Iquid pressure through a suitabledrive arrangement.

2.96 mechanical reaction type vibrationgenerator; unbalanced mass vibrationgenerator : A vibration machine in which the forcesexciting the vibration are generated by rotating orreciprocating unbalanced masses.

2.97 resonance vibration generator: A vibrationgenerator which contains a vibration system whichis excited at its resonance frequency.

2.98 piezoelectric vibration generator : Avibration generator which has a piezoelectrictransducer as its force-generating element.

2.99 magnetostrictive vibration generator: Avibration generator which has a magnetostrict ivetransducer as its force-generating element.

2.100 deadweight; pure mass; lumped mass:A mass having the characteristics of a perfectlyrigid mass over the frequency region of concern.

2.101 cycle (verb) : A device is said to be cycledif it is operated repetitively through a range of acontrolled variable such as frequency. [See eye/e(noun) (2.22).]

2.102 cycle period: The time required to cycle adevice through all the controlled variables in thecontrol range.

2.103 cycle range: Cycle range is defined by theminimum and maximum values of the controlledvariable, such as frequency, between which thedevice is cycled.

2.104 sweep (as applied to the operation of avibration generator) : The process of traversingcontinuously through a range of values of anindependent variable, usually frequency.

2.105 sweep rate : The rate of change of theindependent variable, usually frequency, forexample dfldr where~ is frequency and t is time.

2.106 uniform sweep rate; linear sweep rate: Asweep rate for which the rate of change of theindependent variable for a sweep, usuallyfrequency, is constant, i.e. dfidt = constant. [Seesweep rate (2.105).]

2.107 logarithmic frequency sweep rate : Asweep rate for which the rate of change offrequency per unit of frequency is constant, i.e.

1S11717 :2000\SO 2041:1990

(dJIJ/dt = constant. [See sweep rate (2.105).]

NOTES

1 For a logarithmic sweep rate, the time to sweep betweenany two frequencies of fixed ratio is constant.

2 It is recommended that logarithmic sweep rate beexpressed in octaves per minute.

2.108 cross-over frequency (in vibration ~environmental testing): That frequency at which acharacteristic of a vibration changes from onerelationship to another.

NOTE — For example, a cross-over frequency maybe thatfrequency at which the vibration amplitude, or r.m.s. value,changes from a constant displacement value versusfrequency to a constant acceleration value versusfrequency.

2.109 isolator: A support, usually resilient, thefunction of which is to attenuate the transmissionof shock and/or vibration.

NOTE — An isolator may include collapsible parts, servo-mechanisms or other devices in lieu of, or in additionto, theresilientmember.

2.110 vibration isolator: An isolator designed to

attenuate the transmission of vibration in afrequency range.

2.111 shock isolator : An isolator designed to

protect a system from a range of shock motions orforces.

2.112 centra-of-gravity mounting system : A

centre-of-gravity mounting system exists if, whenthe mounted equipment is displaced by translationfrom its neutral position, there is no resultant

moment about any axis thrtwgh the centre of mass.

NOTE — In an ideal case, ifan equipment is supportedby acentre-of-gravity mounting system, then all natural (rigid-body) modes ofvibrationof the equipmenton its mountsaredecoupled,Translationalmotionsof excitation willnot exciterotationalmodes ofvibrationand vice versa. In practice, thisis very difficultto achieve.

2.113 shock absorber : A device for thedissipationof energy inorder to reduce the responseof a mechanical system to applied shock.

2.114 damper; absorber : In vibrationapplications, a device used for reducing themagnitude of a shock or vibration by energydissipation methods.

2.115 snubber : A device used to restrict therelative displacement of a mechanical system byincreasing the stiffness of an elastic element inthe system (usually abruptly and by a large factor)whenever the displacement becomes larger than aspecified amount.

15

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2.116 dynamic vibration absorber : a devicefor reducing vibrations of a primary system over adesired frequency range by the transfer of energyto an auxiliary system in resonance so tuned thatthe force exerted by the auxiliary system isopposite in phase to the force acting on the primarysystem.

NOTE — Dynamic vibration absorbers maybe damped orundamped, butdamping is not the primary purpose,

2.117 detuner: An auxiliary vibratory system withan amplitude-dependent frequency characteristicwhich modifies the vibration characteristics of themain system to which it is attached.

NOTE — An example is an auxiliary mass controlled by anon-linearspring,

3 Mechanical shock

3.1 mechanical shock shock: A sudden changeof force, position, velocity or acceleration thatexcites transient disturbances in a system.

NOTE — The change is normally considered sudden if ittakes place in a time that is short compared with thefundamental periodsof concern.

3.2 shock pulse : A form of shock excitationcharacterized by a sudden rise and/or sudden decayof a time-dependent parameter (such as motion,force or velocit y).

NOTE — A descriptivemechanical term shouldbe used, forexample acceleration shock pulse.

3.3 applied shock; shock excitation : Anexcitation, applied to a system, that produces amechanical shock.

3.4 shock motion : A transient motion causing,or resulting from a shock excitation.

3.5 impact: A single collision of one mass with asecond mass.

3.6 impulse :

(1) The integral with respect to time of a forcetaken over the time during which the force isapplied.

(2) For a constant force, the product of the forceand the time during which the force is applied.

NOTE — In shock usage, the time intervalis relativelyshort.

3.7 bump : A form of shock which is repeatedmany times for test purposes.

3.8 ideal shock pulse : A shock pulse that isdescribed by a simple time function, for examplethose defined M 3.9 to 3.15.

3.9 half-sine shock pulse: An ideal shock pulsefor which the time-history curve has the shape ofthe positive (or negative) section of one cycle of asine wave.

3.10 final peak sawtooth shock pulse; terminalpeak sawtooth shock pulse: An ideal shock pulse ,,for which the time-history curve has a triangularshape for which the motion increases linearly to amaximum value and then drops instantaneouslyto zero.

3.11 initial peaksawrtooth shock pulse: An idealshock pulse for which the motion risesinstantaneously to a maximum value, after whichit decreases linearly to zero.

3.12 symmetrical triangular shock pulse: Anideal shock pulse for which the time- histoty curvehas the shape of an isosceles triangle.

3.13 versine shock pulse; haversine shockpulse: An ideal shock pulse for which the time-history curve has the shape of one full cycle of aversine curve beginning at zero (sine-squaredcurve).

3.14 rectangular shock pulse: An ideal shockpulse for which the motion rises instantaneouslyto a given value, remains constant for the durationof the pulse, then instantaneously drops to zero.

3.15 trapezoidal shock pulse: An ideal shockpulse for which the motion rises linearly to a givenvalue, which then remains constant for a period oftime after which it decreases tb zero in a linearmanner.

3.16 nominal shock pulse; nominal pulse: Aspecified shock pulse that is given with specifiedtolerances.

NOTES

1 “Nominal shock pulse” is a generic term. It requires anadditionalmodifierto make its meaning specific, for examplenominal half-sine shock pulse, or nominal sawtooth shockpulse,

2 The tolerances of the nominalpulse from the ideal maybeexpressed in terms of pulse shapes (including area), orcorrespondingspectra.

3,17 nominal value of a shock pulse: A specifiedvalue (for example peak value or duration) givenwith specified tolerances.

3.18 duration of shock pulse: The time-intervalbetween the instant the motion rises above somestated fraction of the maximum value and theinstant it decays to this fract ion.

16

NOTES

1 This definitionis limited to pulses of simple shape.

2 Formeasured pulses, the “statedfraction”is usuallytakenas 1/10, For ideal pulses, it is taken as zero.

3.19 rise time; pulse rise time: The interval oftime required for the value of the pulse to rise fromsome specified small fraction of the maximumvalue to some specified large fraction of themaximum value.

NOTE — Formeasured pulses,the “specifiedsmall fraction”is usually taken as 1/10 and the “specifiedlarge fraction”as9/10. For ideal pulses, the fractions are taken as Oand 1,0.

3.20 pulse drop-off time; pulse decay time:The interval of time required for the value of thepulse to drop from some specified large fractionof the maximum value to some specified smallfraction of the maximum value.

NOTE — See the note to 3.19.

3.21 blast; air blast; underwater blast : Thepressure pulse and associated air or water motionresultingfrom an explosion or other sudden changeof pressure in the atmosphere or water.

3.22 shock wave : A shock time history(displacement pressure or other variable)associated with the propagation of the shockthrough a medium or structure.

NOTE — In liquids and gases, a shock wave is usuallycharacterized by a wave front in which the pressure risessuddenlyto a relatively large value.

3.23 shock testing machine; shock machine:A device for subjecting a system to controlled andreproducible mechanical shock.

3.24 shock response spectrum:

(1)The description of the responses to an appliedshock of a series of systems of a specified typeas a function of their natural frequencies.

(2) As used in the field of mechanical shock, anexpression that approximates the maximumresponses (displacement, velocity or acceleration)to an applied shock of an assembly of linear singledegree-of-freedom systems, as a function of theirnatural frequencies.

NOTES

1 “Shockresponse spectrum”is a generic term. It requiresan additional modfier to make its measuring specific, forexample acceleration or velocity or displacement shockresponse spectrum.

2 If the amount and type of damping of the systems are notgiven, they are assumed to be zero. Unless otherwiseindicated, the responses are maximum absolute valuesirrespective of sign and the time at which the maximum

IS11717 :2000ISO 2041:1990

occurs.This is often referredto as maximax shock responsespectrum. If reference is made to other types of shockresponse spectra, this shall be stated.

3 It should be noted that the concept of a shock responsespecturrnisnotfullyconsistentwiththe definitionof spectrum( see 1.56).

4 Transducers for shock and vibrationmeasurement

4.1 transducer : A device designed to receiveenergy from one system and supply energy, ofeither the same or of a different kind, to another insuch a manner that the desired characteristics ofthe input energy appear at the output.

4.2 electromechanical pick-up : A transducerwhich is actuated by energy from a mechanicalsystem (strain, force, motion, etc), and suppliesenergy to an electrical system, or vice versa.

NOTE —The principaltypes of transducersused invibrationand shock are

a)

b)

c)

d)

e)

f)

9)

h)

i)

j)

k)

1)

piezoelectric accelerometer

piezoresistive accelerometer

strain-gauge type accelerometer

variable-resistance transducer

electrostatic (capacitor) (condenser) transducer;

bonded-wire(foil)strain-gauge;

variable-reluctance transducer;

magnetostrictiontransducefi

moving-conductortransduce

moving-coiltransduce

inductiontransduce~

electronic transducer.

4.3 seismic pick-up: A transducer consisting ofa seismic system inwhich the dfierential movementbetween the mass and the base of the systemproduces an electrical output.

NOTE — Acceleration pick-ups operate in a frequencyrangebelow the significantnatural frequency of the seismicsystem. Velocity and displacement pick-ups operate in afrequency range above the natural frequency of theseismic system.

4.4 linear transducer: A transducer for whichthe output quantity and’the inputquantity are linearlyrelated within a specified frequency and amplituderange.

4.5 unilateral transducer : A transducer thatcannot be actuated by signals at its outputs in sucha manner as to supply related signals at its inputs.

17

1S11717 :2000ISO 2041:1990

4.6 bilateral transducer: A transducer capableof transmi~ion in either direction between itsterminations.

NOTE — A bilateraltransducerusuallysatisfiesthe principleof reciprocity.

4.7 sensing element: That part of a transducerthat is activated by the input excitation and suppliesthe output signal.

4.8 rectilinear transducer: Atransducerdesignsdto be sensitive to some characteristic of a

translational motion.

NOTE — The modifier “rectilinear”is used only when it isnecessay to distinguishthis type of transducer from thosesensitive to rotationalmotions,

4.9 angular transducer: A transducer designedto measure some characteristic of rotationalmotion.

4.10 accelerometer; acceleration pick-up : Apick-up which converts an input acceleration to anoutput (usually electrical) that is proportional to theinput acceleration.

4.11 velocity pick-up : A pick-up that convertsan input velocity to an output (usually electrical)that is proportional to the input velocity.

4.12 displacement pick-up : A pick-up thatconverts an input displacement to an output(usually electrical) that is proportional to the inputdisplacement.

4.13 vibrograph : An instrument, usually self-contained and mechanical in operation, that canpresent an oscillographic recording of a vibrationwaveform.

4.14 vibrometer : An instrument capable ofindicating on a scale some measure of themagnitude of a vibration, such as peak velocity,r.m.s. acceleration, etc.

4.15 sensitivity (of a transducer) :The ratio of aspecified output quantity to a specified inputquantity.

NOTE—The sensitivityof a transducerisusuallydeterminedforsinusoidalexcitation.

4.16 calibration factor (of a transducer) : The

average sensitivity within a specified frequencyrange. [See sensitivity (4. 15).]

4.17 sensitive axis (of a rectilinear transducer):The nominal direction for which a rectilineartransducer has the greatest sensitivityy.

4.18 transverse axis (of a transducer) : Anynominal direction perpendicular to the sensitiveaxis.

4.19 transverse sensitivity (of a rectilineartransducer); cross-sensitivity: The sensitivityy of.a transducer to excitation in a nominal directionperpendicular to its sensitive axis.

NOTE —The transverse sensitivity is usually a functionofthe nominaldirectionof the axis chosen.

4.20 transverse sensitivity ratio (of a rectilineartransducer); cross-sensitivity ratio: The ratio ofthe transverse sensitivity of a transducer to itssensitivity aiong its sensitive axis.

4.21 transducer phase shift :The phase angiebetween the transducer output and input forsinusoidal excitation.

4.22 transducer distortion : Distortion whichoccurs when the output of the transducer is notproportional of the input.

4.23 ampiitude distortion (of a transducer) :Distortion occurring when the ratio of the output ofa transducer to its input at a given frequency varieswith the input ampiitude.

4.24 frequency distortion; frequency response:Distortion or response occurring within a givenfrequency range when the ampiitude sensitivity ofthe transducer for a given ampiitude of excitationis not constant over that range.

4.25 phase distortion: Distortion occurring whenthe phase angie between the output of a transducerand its input is not a iinear function of frequency.

5 Data processing

5.1 power spectrai density; auto-spectraidensity; auto spectrum : The power spectraidensity G (f) of a quantity ~ (t) is the mean-squarevaiue of that part of the quantity passed by a narrow-band filter of centrefrequency~ per unit bandwidth,in the iimit as the bandwidth approaches zero andthe averaging time approaches infinity.

NOTES

1 Powerspectral density can be expressed as

lJ~2G(~)=lim ~jj ~ g(ft, B)dt

B,+OT+w

where

&*~ t,B ) is the resultof passing &(t) througha narrow-band-pass filter of bandwidthB centred at~ and thensquaringthe output;

T is the aver’ging time.

18

in terms of Fourier transforms, G (f) can be expressed as

G(fi=lim~ F(~T) 2T+~

where

f ‘?0

F(j T) = ~OTg (f) e-i2’fi dt

2 Powerspectral de&ity is a generic term used regardlessof the physical process represented by the time-history.The physical process involved is indicated in referring toparticulardata.

For example, the term acceleration power spectraldeneity or acceleration spectral deneity is used insteadof power spectral density when the acceleration spectrumis to be described.

3 For stationary processes, the power spectral density istwice the Fouriertransform [see Fourierspectrum (A.21)] ofthe autocorrelation function, and maybe expressed as

G(J) = 2 ~mR (t) e ‘i2”fidt

= 4jOm~(f) cos(27@)dt(~ 20 )

5.2 power spectrum : A spectrum of mean-squared spectral density values.

5.3 cross-spectral density; cross-spectrum :Complex valued function of frequency J of twoquantities g, (~) and g, (t) defined by

G1,2(f) =C1,2(f)-iQ1,2 (f)

where

the real part Cl, ~ (f), called the coincidentspectral density function (or co-spectrum), isthe average product of ~1 (t) and $2 (t) atfrequency f per unit bandwidth, for anappropriate bandwidth B and averaging time2’.The real part, Cl, * (f), is thus given by thefollowing equation:

where

& V f, @ and & V f, B) are the results ofpassing <1 and 62 (t), respectively, throughidentical narrow-band-pass filters of bandwidthB centred at f;

the imaginary part Q,, z(f), called the quadraturespectral density function (or quad-spectrum), isalsoan average product of g, (t) and g2(r) at frequencyJper unit bandwidth, except that f2 (t) is shifted inphase to produce a 90° phase lag. The imaginarypart, Q,, z (f), is thus given by the following

1S11717 :2000ISO 2041:1990

equation:

Ql,2(f’)=lim : ~T&(LLB);~(fXB)df

B+OT-+@

where

~1 (L t, @ k3theresult of passing g, (r) througha narrow-band-pass filterof bandwidthB centredat J

f~~ t, B) denotes a 90° phase lag from;2 ~ t,B) which is the result of passing g2(t) througha narrow-band-pass filterof bandwidthB centredat$

NOTES

1 For the definitions of the function G (f), see the notesunder power spectrtd density (5.1).

2 The functionsCl, z (f) and Ql, z~ can ben expressed interms of Fourier transforms as follows:

Cl, z(f) =lim $ Re[F;(t T). Fz(f T)]T+m

Q,,2~)=lim $ /m [F”: M T). Fz K T)]

T+.

where

/2 ();

F;(t T) =~T &(l)ei2’fidt;o

F2~ T) = ~T 42(f)e-i2’fidt;o

Re [...] and Im [...]are the real and imaginaryparts,respectively,of the function in the brackets.

3 In terms of finite Fourier transforms, Gl, z(f) can beexpressedas

GI,2(f) =Iim -$ [F; (f T)FzVZ T)]T-+ m

4 In terms of the Fourier transform of the cross-correlationfunction (RI,J, Gt,z (J) canbe expressed as

G1,2(~)=2 J~~ RI,z(l) e+2Xfldt

5.4 coherence function: The ratio of the squareof the absolute value of the cross-spectral densityfunction to the product of the spectral densityfunctions of the two quantities g,(t) and;2 (t).

The coherence function is given by the followingexpression:

lGl,2(n127f,2(n=

Gl(f) . G2(n

At any frequency~ the coherence function satisfieso<y:,2(f)<l.

19

1S11717 :2000ISO 2041:1990

NOTE — Fordefinitionsof the terms GI, z (f), Cl (f) and Gz NOTE — For example, smoothingover three data points is(f), see the notes under power spectral density (5.1) and characterized by the relationshipcross-spectra/ density (5.3).

~k= (Xk.i +Xk+Xk+l)/35.5 statistical degrees of freedom: The numberof independent variables in an estimate of some

Smoothingcan be done in the time domain, the frequencydomain and in histograms,

auant itv..

NOTES5.18 truncation (in vibration analysis) : Theapplication of a record length which is too short to

1 The number of degrees of freedom determines the define the signal accurately.statisticalaccuracy of an estimate.

5.19 data processing : A general term for the2 When time-averaging is used in the analysis of randomdata, the effective number of statistical degrees of freedom

electronic or mechanical processing of original

iS n = ~T, where B is the effective filter bandwidthand Tisinformation.

the effective averaging time, 5.20 data handling : Data processing which

5.6 equivalent (static) acceleration (for a single introduces no change in the original information,

degree-of-freedom system) : For a dynamic for example card sorting tabulation, storage,

excitation, the steadily applied acceleration required retrieval, coordinate transformation, etc.

to produce the same maximum relativedisplacement as the excitation does.

5.21 data reduction : Data processing whichcauses changes in the original information, for

5.7 pseudovelocity: The product of the maximum example conversion from analogue to digital or vice

relative displacement of an undamped single versa, inversion of a function, averaging, etc.

degree-of-freedom system and the angular natu-mlfrequency 27t~n.

5.22 real-time analysis : Signal processing toanalyse parameters in realtime.

5.8 aliasing error: An erroneous result in digital 5.~3 Fast Fourier Transform (FFT) : A processanalysis of signals causal by having the maximumfrequency of the signal greater than one-half the

where the computing _times of complex

value of the sampling freuuencv (see 5.15)multiplications/additions are greatly reduced.

(which is sometimes re~erred”to as ~he “Shannon 5.24 quantizing: An analog-to-digital conversionfrequency”). where sampling quantizes every data point.

5.9 data block : The ordered collection of data 5.25 window function: A truncated function thatpoints stored in the memory of a digital computer. is used for reducing the errors in processing

5.10 block size; block length : The number ofweighted data points.

records, words or characters in a block. 5.26 deterministic vibration : A vibration the

5.11 data points :The digital values obtained asinstantaneous value of which at a certain time canbe predicted from knowledge of its time history at

a result of converting an analog signal. an earlier time.

5.12 frequency resolution: The reciprocal of the NOTE — In mathematical terms, if f (f ) for r > tocan betotal time (see 5.1 3). predictedfromf(~) for t c ~o,then the vibration represented

5.13 total time (in data processing) : The timebyf(~) is deter-mi&tic.

needed to fill a data block. 5.27 time history: The magnitude of a quantity

5.14 sampling; sample (verb) : To obtain theexpressed as a function of time.

values of a function for regularly or irregularly 5.28 stationary process : An ensemble of time

spaced distinct values from its domain. histories such that their statistical properties are

NOTE — Other meanings of this term may be used ininvariant with respect to translations in time.

particularfields, for example in statistics. - 5.29 strongly self-stationary : Term used to

5.15 sampling frequency : The number of describe a random signal if all statistical properties

samples taken in one second. determined by averaging a sample over a finitetime interval are independent of the time at which

5.16 sampling interval: The time interval between the sample occurs. ‘two samples.

5.30 weakly self-stationary : Term used to5.17 smoothing: An averaging process in which describe a random signal if the mean value anda data block is shifted and averaged. autocorrelation function determined by averaging

20

1S11717 :20001s0 2041:1990

a sample over a fin’ te time interval is independentof the time at whit the sample occurs.

5.31 ergodic p cess : A stationary processcontaining an ens lbleof time histories where timeaverages are thl me for every time-history.

NOTE — If follows these time averages from any timehistory will then b qual to corresponding statisticalaverages over the en> !mble.

5.32 random process; stochastic process: Aset (ensemble) of time functions that can becharacterized through stat istical properties.

5.33 ensemble; set: A collection of signals.

5.34 autocorrelation function : For a quantityx(f), the mean of the product of the value of thequantity at time t with its value at time (t+ r).

NOTES

1 The autocorrelation function can be expressedmathematically as

R (z) = [x(t)] [X(f + ~)] = ~ ~’TX(l) X(f + z) dr

2 For a stationary random quantity x(t) which persists forail time, Tapproaches infinity,that is

R (~)= Iim ~jTx(t) x(t + T) dt

T-CO O

In practice, T is finite and the formula given in note 1 onlygives an estimate with a certain statistical uncertaintywhich increases as Tdecreases.

5.35 cross-correlation function : For twoquantities x(t) andy (t), the mean of the product ofthe value of one function at a time tand the valueof the other function at a time (t+ z).

NOTES

1 The cross-correlation function can be expressedmathematically as

2 See note 2 under autocorrelation function (5.34).

5.38 autocorrelation coefficient: For a quantityx(t), the ratio of the autocorrelat ion funct ion tot hcmean-square value of the quantity.

NOTE —The autocorreiation coefficient can be expressedmathematicallyas

R(I) [X(t)][x(f + T)]Q(T)=— =

R(0) .%

5.37 cross-correlation coefficient : For twoquantities x(t) and y (t), the ratio of the cross-correlation function to the square root of the productof the mean-square values of the quantities.

NOTE — This can be expressed mathematically as

QX,J’(T)= R‘Y(T)JimiGi

where

Rx(o)= 2??,

R, (o)=?-

Rx,~(T) is as defined in 5.35.

Atany deiay t, the cross-correlation coefficientsatisfies

-l< QX,Y(Z)S1

5.38 effective bandwidth (of a specified band-pass filter): The bandwidth of an ideal filter whichhas flat response in its passband and transmitsthe same power as the specified filter when thetwo fittersreceive the same whtie-noise input signal.

NOTE — The effective bandwidth may be measured bydividing the mean-square response of the fiiter to white-noise excitation by the product of the excitation siectraldensity and the equare of the maximum transmission.

5.39 effective averaging time :The time requiredfor an ideal integrator to yield the same parameterestimate as the averaging device employed.

5.40 confidence interval : For a normaldistribution of measured data points, the rangewithin which one value will lie with a given degreeof probability.

21

1S11717 :2000ISO 2041:1990

Annex A(informative)

Mathematical termsil

A.1 reference: A quantity associated with a pointinan element or system from which, or with respectto which, other similar quantities are measured. Ifthe same reference is used generally throughout asystem, it is called a common reference.

A.2 variable: A quantity that can assume a (finiteor infinite) succession of values.

A.3 independent variable: A variable, such astime, the value of which is not determined by othervariables.

A.4 dependent variable: A variable the valuesof which are determined by values of independentvariables and parameters.

A.5 parameter: In a mathematical relationship, aquantity that describes a system characteristic. Aparameter may be a variable in an equation, or itmay be a “constant” that can be assigned differentvalues.

A.6 function : The expression of a relationshipbetween one dependent variable (the value of thefunction) and one or more independent variablesand constants. For example a function of y, z

and r.

A.7 proportional : One variable is said to bedirectly proportional to another variable if the ratioof the corresponding values of the variables isconstant, and inversely proportional to anothervariable if the ratio of the reciprocal of one variableto the corresponding value of the other variable isconstant.

A.8 linear function : One variable is said to be alinear function of another variable if changes inthefirst variable are directly proportional to changesin the second variable.

A.9 generalized coordinates : Quantitiesindependent of one another, and necessary andsufficient for describing the configuration of asystem.

A.1 O vector : A quantity that is completelydetermined by its magnitude and direction.

A.11 scalar : Any quantity that is completelydetermined by its magnitude.

A.12 imaginary number: The product of a real

number and=. The ~ is normallyrepresented by j or i.

NOTES

1 The positivevalue of the square root is implied.

2 In thevector,orgeometric,interpretation,the multiplicationof any complex number by i rotates it 90° counterclockwiseabouttheorigin,and multiplyingitby- i rotatesit90° clockwiseabout the origin.

A.13 complex number:

(1) A number that contains both a real and animaginary part.

(2) A number which represents a vector from theorigin in a two-dimensional ccmrdinate system.

NOTE — If a complexnumberis givenas z = x + iy,where theimaginary part is given as iy, then x and y represent thecomponent parts of the vector along the two orthogonal xand iy axes. The magnitude of the vector (or absolutevalue of the complex number) is Z = (# + ?)1/2 and thedirection of the vector (or the argument of the complexnumber) is 0= arc tany/x, The complex number can also beexpressed as

z= Z(cos@+isin@=Zeio

A.14 phasor: A complex number the magnitudeof which is the amplitude of the oscillation and theangle of which is the phase. For example, if it isdesired to express a harmonic oscillationY (t) = Y. COS( @ + @ ) in complex notation, itwould be expressed as follows:

Y(t) = Re(Yle/@)

where

YI is a complex quantity called the phasor, themagnitude of which equals Y. and the angle(or argument) of which is the phase angle (@);

Re means “real part of”, but this is usuallyomitted as understood.

Y1 is expressed as

Yl)<@

or

Yocos@+i YOsin@

where i = ~.

Y1may also be written Y1= YOe’?

1) The definitions included in this annex are essential to those working in the field of vibration and shock. However,as theformulationsare also the concern of others, these definitionsare notconsidered part of this International Standard.

22

1S11717:2000ISO 2041:1990

A.15 argument (of a complex number): The anglethat fixes the direction of the complex number(vector). [See the note under comp/ex number(A.13).]

A.16 modulus (of a complex number) : Theabsolute value of the complex number. [See thenote under comp/exnumber(A.l 3).]

A.17 absolute value

(1) Of a real number, a positive number that hasthe same numerical value as a real number whichmay be of either sign.

(2) Of a complex number, the positive square rootof the sum of the squares of the real and imaginaryparts. [See the note under comp/exnurnber(A.l 3).]

A.18 Fourier series: A series which expressesthe values of a periodic function in terms of discretefrequency components that are harmonicallyrelated to each other.

NOTES

1 A non-periodic functioncan be represented by a Fourierseries if the interval over which the function is defined istaken as the fundamental period of the series.

2 A Fourier expansion off(t) intoa Fourier series is givenby

f(l) =w+ ~ (a. cosnco/+ bflsin mix))1=1

A Fourier expansion off(t) intoa complex Fourierseries isgiven as

H=l

where

an and b. are Fourier coefficients;

C“is a complex Fourier coefficient;

aJis the angular frequency and is equal to 2n/~, wherer is the fundamental period;

n is assigned only integralvalues.

The values of the Fourier coefficient are

bn= ~ \T’(f) sin~~d~(n= 1,2, 3, ....)o

c.= ~ $J(t) e-htidt(n=tl, *2, *3, ....)

It can be shown that

an - ih % - ibnc+n=— co=ao c-n=

2 2

The amplitude of each Fourier discrete frequency is

‘.=-

The Fourier phase angle is

%= arctan(*)A.19 Fourier coefficients : The coefficients ofthe discrete harmonic components of a Fourierseries. [See note 2 under Fourier series (Al 8). ]

A.20 Fourier transform; Fourier integralequation:

(1) Direct Fourier transform :The transformationof a non-periodic function of time (or other variablesuch as distance) into a continuous function offrequency (or other variible such as wave number).

(2) Inverse Fourier transform :The transformationof a continuous function of frequency (or othervariable such as wave number) into itscorresponding function of time (or other variablesuch as distance).

NOTE — Iff(t) isa non-periodicfunctionof time, thecomplexform of the direct Fourier transform equation is:

F(m)= J+mf(t)e-id dt–co

The time function~(t) is obtainedfromF(o) bythe followingintegration(the inverse Fourier transform equation):

1 +m

(The use of the factor l/27t represents one formulationof the pair of transforms. In other formulations l/2nappears in the direct ratherthan the inverse transform,or 1d2n may appear in each.)

Since F (co) is in general in complex form, it can bewrittenin terms of a real and an imaginary part:

F (CO)= fle[~ (o)] + i Im [F(o.$]

where

Alternatively, the Fourier spectrum can be defined interms of its absolute value and phase angle, lF(aI) Iand UI(o), respectively:

F(o)= IF(o.J)Iei~

where

IF (fD)!= ~Fie2[F’(o)]+Irn2[F(@)]

‘(”)=arctan{:%}A.21 Fourier spectrum: A description of Fourieramplitudes as a function of frequency.

NOTE — Two Fourier spectra are required to define a

23

..

1S11717 :2000ISO 2041:1990

function.These can either be spectra of the ~mplitudes ofthe real and imaginary parts of a Fourier spectrum or theycan be a spectrum of the absolute amplitude values and aspectrum of the fourier phase angles. [See note 2 underFourier series (A,18) and the note under Fourier transform(A,20),]

A.22 Fourier phase spectrum; phase s~rum:The description of Fourier phase angle as a functionof frequency [See note 2 under ~o~rier series(A.18) and the note under Ewriertransforrn (A.20).]

A.23 line spectrum: A spectrum the componentsof which occur at one or more discrete frequencies.

A.24 continuous spectrum : A spectrum thecomponents of which are continuously distributedover a frequency range.

A.25 orthogonal functions: A set of functions,0. (x), defined in an interval Os x <x, is orthogonalin the interval if

J~@.@idx=O, forn#m

where

CD.* is the complex conjugate of @m.

A.26 deterministic function: A function the valueof which can be predicted from knowledge of itsbehaviour at previous times.

A.27 superposition principle: A principle whichstates that the responses of a system to differentexcitations are additive. The superposition principle

is valid only for linear systems.

A.28 process : A collection of signals. The term“process”rather than the term “ensemble” ordinarilyis used when it is desired to emphasize theproperties the signals have or do not have as agroup. Thus, one speaks of a stationary proceserather than of a stationary ensemble.

A.29 probability: An expression of the likelihoodof occurrence of an event. The probability ofoccurrence of a particular event is generallyestimated as the ratio of the number of occurrencesof the particular event to the total number ofoccurrences of all types of events considered.

For a stationary random vibration, the probabilitythat the magnitude will be within a given magnituderange is taken to be equal to the ratio of the timethat the vibration is within that range to the totaltime of observation.

NOTES

1 It is required that a large number of events or a longobservationtimebe involvedinthe probabilitydeterminations.

2 A unitprobabilitymeans that theoccurrenceofa particularevent is certain, Zero probabilitymeans that it willnotoccur.

3 The probability that the magnitude of a vibration will bewithina given range is equal to the integralof the probabilitydensity function of that vibration integrated over the givenrange. [See probability density (A,30).]

A.30 probability density: As applied to vibrationtheory, at a specified vibration magnitude, the ratioof the probability that the vibration magnitude willbe within a given incremental range, to the size ofthe incremental range, as the increment sizeapproaches zero.

NOTES

1 The probability density can be expressedmathematically as

P(Axm)p(x.) = Iim —

Axm-+o Axm

or

~(xl_ w(x)(lx

where

P(XJ ia the probabilitydensity at x~;

Ax~is an incremental range of magnitude beginningat a magnitudex~;

p(AxJ isthe probabilitythat the vibration magnitudewill have a value between x~ and X“ + AX~,

2 The probabilitydensity is the derivative of thecumulative probabilitydistributionfunction,P(x), withrespect to X. (See A.34).

A.31 probability density function; probabilitydensity distribution curve : The probabilitydensity function, for vibration theory, is anexpression of the probability density associatedwith a stated vibration.

The probabi~ty density distribution curve is agraphical representation of the probability densityfunction.

NOTES

1 The functionsp(x) given under probability density (A.30)norms/ distribution (A.32) and Ray/eigh distribution (A.33)are probabilitydensity functions.

2 The totalarea underthe probabilitydensity“curveis equalto unity.

A.32 normal distribution; Gaussiandistribution; normal probability densitydistribution: A normal, or Gaussian, distributionhas a probability density function equal to

P(%) =

where;e”(s 2X

.J#(2d)

a is the r.m.s. value of, for instance, vibrationmagnitude [see standard deviation (A.37).]

XP is the instantaneous vibration magnitude.

24

Is 11717:2000ISO 2041:1990

The mean value of the vibration is assumed to be NOTE — The r,m.s. value of a set of numbers can be

zero. represented as

A.33 Rayleigh distribution : A Rayleighdistribution has a probability density function equalto

‘Pp(xp) . ~ e –#p/(z&)

awhere

a is the r.m.s. value;

XPis the magnitude of positive maxima.

The maxima (peak values) of a narrow-bandGaussian random vibration have a Rayleighdistribution.

A.34 cumulative probability distributionfunction; probability distribution function: Thecumulative probability distribution function, P(x),

represents the probabilityy that the magnitude ofthe variable x (magnitude of the random vibration)will not be exceeded. It is the probability that thevalue of the variable x will be less than a specifiedvalue, X.

NOTE —The cumulative probabilitydistributionfunctionisequal to

P (X)= ~_x@P(U)du

where u is a dummy variable of integrationforx.

A.35 mean value; arithmetic mean :

(1) Of a number of discrete quantities, the algebraicsum of the quantities divided by the number ofquantities.

NOTE — The mean value, x, is given by

z’”F= ~

where N

Xflis the value of the nth quantity;

N is the total number of discrete quantities,

(2) Of a function, x(t), over an interval between t,and t2, the mean value, X is given by

A.36 geometric mean (of two quantities) : Thesquare root of the product of two quantities.

[1; ~zm %

r.m.s. value= —N

where the subscript n refers to the nth number of whichthere are a total of N.

(2) Of a single-valued function,f(t), over an intervalbetween tl and t2, the square root of the averageof the squared values of the function over theinterval.

NOTES

1 The r.m.s, value of a single-valued function,~(f), over aninterval between (1and tz is

pt?

1‘/2

r.m.s. value = tl/(t)zdf

L 12-tl J

2 Invibrationtheory,the mean value of the vibrationis equaltozero. In this case, the r.m.s.value is equal to the standarddeviation,andthe mean-squarevalue isequal tothevariance(62). [See standard deviation (A.38) and variance (A.39).]

A.38 standard deviation: The root-mean-square(r.m.s.) value of the deviation of a function (or aset of numbers) from a mean value.

NOTES

1 The symbola is commonlyused to representthestandarddeviation.

2 For a set of numbers, the standard deviation is

[n‘n -i)1

2 1/2

‘“h 1where

the subscriptn refers to the nth numbeu

N is the total number of numbers in the set

Z is the mean value of the set. [See mean value(A.35).]

3 If x is a single-valued functionof t, its standard deviationover an interval between ~1and tz is

[1Jtz 1/2

(x- F)’cfttl

0=t2 - t,

4 In vibration theory, if the mean value, 7, is taken to bezero, then the standarddeviationis equal to the r.m.s.value.

A.39 variance : The square of the standarddeviation.

A.37 root-mean-square value; r.m.s. value: NOTE — In vibration theory, where the mean value is zerothe variance is the mean-square value of a variable

(1) Of a set of numbers, the square root of the representingthemagnitudeof a vibration.[See note3 under

average of their squared values. mean-square va/ue (A.40).]

25

1S11717:2000ISO 2041:1990

A.40 mean-square value: The mean-square valueof a function (or set of numbers) over an interval isequal to the mean of the squared values of thefunction (or set of numbers) over that interval.

NOTES

1 The mean-square value is the square of the r.m.s, value.

2 In vibration theory, when the mean value is zero, the

mean-square value is the variance. [See vafiance (A.39).].

If the mean value is not zero, then

l/2. $+#

where

vz is the mean-square value;

a2 is the variance;

F is the mean value,

Annex B(informative)

Auxiliary terminology)

B.1 signal :

(1) A disturbance variation of a physical quantityused to convey reformation.

(2) The information to be conveyed over acommunication system.

B.2 distortion (of a signal): An undesired changein the waveform.

NOTE — For an acceleration, for example, the distortion,d, is usually expressed in percentage terms as

d= II a~otfia.f ~ ,00

alwhere

m is the r.m.s. value of the acceleration atthe driving frequency;

atd is the total r.m.s. value of the accelerationapplied (including the value of al).

B.3 resolution :The resolution of a system formeasuring motions is the smallest change in inpui(dispalcement, velocity, acceleration, strain, orother input quantity) for which a change in outputis discernible.

B.4 time constant; relaxation time: The timetaken by an exponentially decaying quantity todecrease in magnitude by a factor of I/e =0,3679.

NOTE —The discharge of an electricalcapacitance througha resistance is proportional to

e-tmc

where

t is time;

R is resistance in ohms;

C is capacitance in farads;

e is the base of natural logarithms;

and the product, RC, is the time constant orrelaxation time.

B.5 ground; earth :

(1)The conducting mass of the Earth, or a conductorconnected to it through a very small impedance.

(2) A conductor that is considered to have zeroelectrical potential. The electrical potential ofthe Earth is usually taken to be zero.

B.6 ground wire; earth wire: A wire connectedto a ground terminal.

B.7 ground loop; earth loop: The closed elec-trical circuit formed by the connection of a groundwire to several ground terminals at differentlocations.

B.8 input impedance (of an electronicamplifier) : The electrical impedance betweenthe input terminals.

NOTE — The input impedance may be affected by theoutput load; if so, the output load should be specified.

B.9 output impedance (of an electronicamplifier): The electrical impedance between itsoutput terminals.

1) The definitionsincluded in this annex are essential to those workingin the field of vibration and shock, However,as theformulationsare also the concern of others, these definitionsare notconsidered partof this International Standard.

26

NOTE — The output impedance maybe affected by thesource impedance at the input;if so, the source impedanceshould be specified.

B.1O operational amplifier: Anamplifier whichincludes a feedback loop which maintains a specificrelationship between the output terminals andthe input terminals.

~OTE — Depending upon the type of feedback and otherauxiliary circuitry, the amplifier can be used to performvarious functions, such as integration, differentiation,charge amplification, etc.

B.11 charge amplifier : An amplifier whichpresents an output that is proportional to thetotal electrical charge presented to the input.

B.12 cross-talk : The signal observed in onechannel due to a signal in another channel.

B.13 frequency response : The output signalexpressed as a function of the frequency of theinput signal. The frequency response is usuallygiven graphically by curves showing therelationship of the output signal and, whereapplicable, phase shift or phase angle as a functionof frequency.

B.14 filter; wave filter: A device for separatingoscillations on the basis of their frequency. Itintroduces relatively small attenuation to waveoscillations in one or more frequency bands andrelatively large attenuation to oscillations of otherfrequencies.

NOTE — Electrical filters, and some mechanical filtersemploying resonances, may amplify selective frequencybands and thus provide filter action. @

B.15 pass band (of a band-pass filter) : Thefrequency band between the upperand lower cut-

off frequencies.

B.16 low-pass filter: A filter which has a singletransmission band extending from zero frequencyup to a finite frequency.

B,17 high-pass filter: A filter which has asingle transmission band extending from somecritical or cut-off frequency, not zero, up to infinitefrequency or, in practice, above the highestfrequency of interest.

B.18 band-pass filter : A filter which has asingle transmission band extending from a lowercut-off frequency greater than zero to a finiteupper cut-off frequency.

B.19 nominal bandwidth (of a filter); bandwidth:The difference between the nominal upper andlower cut-off frequencies. This difference can beexpressed

1S11717 :2000ISO 2041:1990

a) in hertz;

b) as a percentage of the pass-band centrefrequency; or

c) as the interval between the upper and lowernominal cut-offs in octaves.

B.20 nominal upper and lower cut-offfrequencies (of a filter pass-band); cut-offfrequency: Those frequencies above and belowthe frequency of maximum response of a filterat which the response to a sinusoidal signal is3 dB below the maximum response.

B.21 constant-bandwidth filter: A filter whichhas a bandwidth of constant value when expressedin hertz. It is independent of the value of thecentre frequency of the filter.

B.22 proportional-bandwidth filter : A filterwhich has a bandwidth that is proportional tothe centre frequency.

NOTE — Octave bandwidth, one-third octave bandwidth,etc, are typicalbandwidthsforproportional-bandwidthfilters.

8.23 octave : The interval between twofrequencies which have a frequency ratio of two.

NOTE — The interval, in octaves, between any twofrequencies is the logarithm to the base 2 (or 3,322 timesthe logarithm to the base 10) of the frequency ratio.

B.24 one-half Octave; half octave: The intervalbetween two frequencies which have a frequencyratio of 21’2,or 1,414. [Seethe note under octave(B.23).]

B.25 one-third octave; third octave: The intervalbetween two frequencies which have a frequencyratio of21n,or1,2599. [See the hote%nder octave(B.23).]

NOTE — For certain kinds of acoustical measurements itis convenient to space the frequencies in fractions of anoctave, but for extensionsintothe infrasonicand ultrasonicranges it is convenient to use powers of 10. These twoconflicting requirements can be satisfied adequa~ely formost purposes because 21n = 1,259 9 is very nearlyequal to 101/10= 1,2589, the discrepancy being less than0,1 %, This means that ten successive intervals of 1/3octaveare very nearlyequivalenttoa ratioof 10 infrequency.

B.26 one-tenth decade: The interval betweentwo frequencies which have a frequency ratio of10lflOor 1,2589.

NOTES

1 The difference between 1II Odecade and 113octave iSless than 0,1 V. [see th~ note under one-third octave(B.25).] The two bandwidths can therefore be consideredequivalent for practical purposes.

2 The interval, in decades, between any two frequenciesis the logarithm to the base 10 of the frequency ratio.

z?

1S11717 :2000ISO 2041:1990

6.27 octave-bandwidth filter : A band-passfilter for which the pass-band is one octave, i.e.the difference between the upper and lower cut-off frequencies is one octave. [See proporfiona/-bandwicfth fi/ter (B.22).]

6.28 one-third-octave filter; third-octavefi Iter: A band-pass filter for which the differencebetween the upper and lower cut-off frequenciesis one-third octave. [See proportions/-bamfwicMfi/ter(B.22) and the note under one-third octave(B.25).]

B .29 narrow-band f ilter: A band-pass f ilter forwhich the pass-band width is relatively narrow.

NOTE — Whether or not a bandwidth can be considerednarrow is dependent upon the circumstances. For shockand vibration work, it is normally 1/3 octaves or less,

6.30 wide-band filter : A band-pass filter forwhich the pass-band is relatively wide.

NOTE — Whether or not a bandwidth can be consideredwide is dependent upon the circumstances. For shockand vibration work, it is normally greater than one octave.

6.31 centre frequency; nominal pass-bandcentre frequency: The geometric mean of thenominal cut-off frequencies of a pass-band.

$_NOTE — The geometric mean is equal to ~fz , wherefiand f2 are the cut-off frequencies.

6.32 band-elimination filter; band-rejectfilter: A filter that provides a large attenuationfor one frequency band, and little loss forfrequencies outside,of this band,

6.33 tracking filter: A band-pass filter (usuallynarrow-band) the centre frequency of which canbe made to follow a quasi-sinusoid of varyingfrequency.

6.34 crystal filter: A narrow-band filter for whichthe piezoelectric crystal operating at a resonancefrequency is the principal element of the filter.

6.35 magnetostrictive filter: A narrow-bandfilter for which a magnetostrictive element at aresonance frequency is the principal element ofthe filter.

6.36 peak-notch filter: An electrical filtei whichis adjusted so as to change the signal appliedto a power amplifier driving an electrodynamicsvibration generator, such that it willeliminate relativemaxima and minima which appear in the spectrumof the generator output.

NOTE —The relative maxima and minima in the spectrumare usually caused by the mechanical reactions ofmechanical elastic systems that are subjected to thevibration.

6.37 equalization (of an electrodynamicsvibrationgenerator system) : The adjustment of the gainof the electrical amplifier and control system sothat the ratio of the output vibration amplitudeto the input signal amplitude is of constant value(or given values), throughout the requiredfrequency spectrum.

28

1S11717 :20001s0 2041:1990

Annex C(informative)

Schema for arranging vibration terms

The terms inthis vibration terminology are arrangedin accordance with the logic shown in figure C. 1. It

is based on practical rather than theoreticalconsiderations, on the manner in which records ofvibrations (time histories) are collected and howthe information extracted from these records istreated. The two principal categories of vibrationsare based on whether a particular vibration isdeterministic or random.

Deterministic vibration is the class of vibrationsfor which the instantaneous value of the vibrationat a specified time is determined precisely by its\ime history (i.e. the record of its instantaneousvalues) for time values earlier (i.e. less) than thespecified time. Random vibration is the class of~f~brationsfor which the instantaneous value of the

vibration at a specified time cannot be determinedby its time history.

F1‘vibrations

aDeterministic

a

Random

II

IPeriodic Non-periodic

Stationary ergodic Non-stationary

I 1 [Stron@y Weakly

Shusoidal Multi-sinusoidal I_ransient self-stationary sell -alationary

Figure C.1 — Schema for types of vibration

29

IS 11717:2000ISO 2041:1990

Alphabetical index

A

absolute vague . . . . . . . . . . . . . . . . . . A.17absorber . . . . . . . . . . . . . . . . . . . 2.114absorber, dynamic vibration. . . . . . . 2.116absorber, shock....,.,.,.. . . . . . 2.113accelerance . . . . . . . . . . . . . . (see table 1)acceleration . . . . . . . . . . . . . . . 1.03acceleration, equivalent (static) 5.6acceleration power spectral

density . . . . . . . . . . . . . . . . . ,see5.1)

acceleration spectral density ‘see 5.1)acceleration of gravity. 1.04acceleration pick-up ., 4.10accelerometer, . . . . . . . . . . 4.10acoustic noise.....,...,., ... (see 2.6)acoustics . . . . . . . . . . . . . . . . . . . . . 1.10air blast . . . . . . . . . . . . . . . . . . . 3.21aliasing error . . . . . . . . . . . . . . . 5.8ambient vibration . . . . . . . . . . . 2.1samplitude ., ., ., . ., .,.,.,.,. 2.33

amplitude distortion 4.23amplitude, double . . . . . . . . (see 2.33)amplitude, peak . . . . . . . . . . . . . (see 2.33)amplitude, single ., (see 2.33)amplitude, vector. (see 2.33)angle difference, phase. . . . .

angle, phase . . . . . . . . . . . . . . . . ,.,

angular frequency . . . . . . . . . . . ,,.

angular transducer ., . . . . .

antipode . . . . . . . . . . . . . . . . . .

antiresonance . . . . . . . . . . . . .

antiresonance frequency .,

aperiodic motion . . . . . . . . . . .

apparent mass . . . . . . . . . . .

applied shock . . . . . . . . . . . . . . .argument . . . . . . . . . . . . . . . . .

arithmetic mean . . . . . . . . . . . . . . .

audio frequency . . . . . . . . . . . .

autocorrelation coefficient

autocorrelation function .,

auto-spectral density.

auto-spectrum . . . . . . . . . . . . .

axis, sensitive . . . . . . . . . . . . . .

axis, transverse . . . . . . . . . . . .

B

band-elimination filter . . . . . . . . .,

band-pass filter . ., . . . . . . . . . . . . .

band-rejec: filter . . . . . . . . . . . . . . .

bandwidth (of a filter) . . . . . . . .

bandwidth, effective ., . . . .

bandwidth, nominal . . . . . . . . . . . .

beat frequency . . . . . . . . . . . . . . . . . .

beats, . . . . . . . . . . . . . . . . . . . . . . . . .

be. . . . . . . . . . . . . . . . . . . . . . . . . . . .

bilateral transducer .,

blast . . . . . . . . . . . . . . . . . . . . . . . . . .

block size . . . . . . . . . . . . . . . . . . . . .

block length . . . . . . . . . . . . . . . . . . . .

2.32

2.31

2.30

4.9

2.47

2.74

2.75

2.21

1.55

3.3

A.15

A.35

2.67

5.36

5.34

5.1

5.14.17

4.18

B.32

B.18

B.32

B.19

5.36

B.19

2.29

2.28

1.5a

4.6

3.21

5.105.10

blocked effectivemass . . . . . . (seetable 1)blocked impedance . . . . . . . . . . . . . . 1.47broad-band random vibration 2.12bump . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7

c

calibration factor . . . . . . . . . . . . . . . . 4.16central principal axes. . (see 1.32)central principal moments of

inertia . . . . . . . . . . . . . . . . . . . (See 1.32)centrefrequency . . . . . . . . . . . . . . . . B.31centre of gravity . . . . . . . . . . . . . . . . . 1.30centre-of-gravity mounting system . 2.112centre of mass . . . . . . . . . . . . . . . . . . 1.31characteristic mode. . . . . . . . . . (see 2.55)charge amplifier . . . . . . . . . . . . . . . E3.11circular frequency . . . . . . . . . . . . . . . 2.30

circular vibration . . . . . . . . . . . . . . . . 2.45coefficient, autocorrelation . 5.36coefficient, cross-correlation . 5.37coefficient, linear viscous damping 2.84

coefficient, viscous damping 2.64

coefficients, Fourier ., ., ., ., A.19coherence function . 5.4common reference . . . . . . . . . . (see A.1)complex excitation ., 1.36complex Fourier coefficient (aee A.18)complex number . . . . . . . . . . . . A.13complex response . . . . . . . . . . . 1.38complex system parameter . . . . . . . 1.40complex vibration (see 1.36)complex waveform . . . . . . . . . . (see l.36)compliance . . . . . . . . . . . . . . . . . . . .

compressional wave . . . . . . . . . . . . .conditioning . . . . . . . . . . . . . . . .

confidence interval . . . . . . . . . .

constant-bandwidth filter. . . . . .

continuous spectrum . . . . .continuous system . . . . . . . . . . . . .

coupled modes, . . . . . . . . . . . . . .

crest factor . . . . . . . . . . . . . . . .

critical damping . . . . . . . . . . . . .

critical damping, fraction of . . . .,

critical speed, . . . . . . . . . . . . . .

critical viscous damping . . . . .,

cross-correlation coefficient.

cross-correlation function . . . .

cross-over frequency ., . . . . . .

cross-sensitivity . . . . . . . . . . . . .

cross-sensitivity ratio . . . . . . ., .,

cross-spectral density . . . . . ., .,

cross-spectrum . . . . . . . . . . . .

cross-talk . . . . . . . . . . . . . . . . . .

crystal filter . . . . . . . . . . . . . . . .

cumulative probability distribution

function . . . . . . . . . . . . . . . . . . . . .

cut-off frequency . . . . . . . . . . . . ,.,

cycle (noun)..,.,......,.,..

cycle (verb) . . . . . . . . . . . . . . . . . . .

cycle period . . . . . . . . . . . . . . . . . .

cycle range . . . . . . . . . . . . . . . . . . .

cyclic frequency . . . . . . . . . . . . .

D

damped natural frequency . . . .,

damper . . . . . . . . . . . . . . . . . . . . . . . .

damping . . . . . . . . . . . . . . . . . . . . . . .

damping coefficient, linear viscous

1.342.58

1.15

5.40

B.21

A.24

1.29

2.53

2.37

2.85

2.86

2.772.85

5.37

5.35

2.108

4.19

4.20

5.3

5.3

B.12

B.34

A.34

B.20

2.22

2.101

2.102

2.103

2.24

2.81

2.114

2.79

2.64

dampingcoefficient,viscous . .damping,critical . . . . . . . . . . . . . . . .damping,criticalviscous . . . . . . . . .damping, equivalent viscous .

damping, frection of critical . .

damping, linear viscous . . . . . . . . . .

damping, non-linear . . . . . . . . . . . . .

damping ratio . . . . . . . . . . . . . . . . . . .

damping, viscous . . . . . . . . . . . . . . .

data block . . . . . . . . . . . . . . . . . . . . . .

datahandling . . . . . . . . . . . . . . . . . . .

data points . . . . . . . . . . . . . . . . . . . . .

dataprocessing . . . . . . . . . . . . . . . . .

data reduction . . . . . . . . . . . . . . . . .

deadweight . . . . . . . . . . . . . . . . . . . .

decibel . . . . . . . . . . . . . . . . . . . . . . . .

decrement, logarithmic. . . . . . . . . . .

degrees of freedom . . . . . . . . . . . . . .

degrees of freedom, statistical.

dependent variable . . . . . . . . . . . . . .

deterministic function . . . . . . . . . . . .

deterministic vibration . . . . . . . . . . .

retuner . . . . . . . . . . . . . . . . . . . . . . . .

difference, phase angle. . . . . . . . . . .

direct-drive vibration generator

Direct Fourier transform . . . . . . . . . .

direct impedance . . . . . . . . . . . . . . .

direct (mechanical) mobility. . .

2.84

2.85

2.85

2.83

2.66

2.82

2.66

2.66

2.82

5.9

5.20

5.11

5.19

5.212.100

1.58

2.87

1.26

5.5

A.4

A.26

5.26

2.117

2.32

2.94A.20

1.43

1.51directly proportional . . . . . . . . . . . (see A.7)

displacement . . . . . . . . . . . . . . . . . . . 1.1

displacement pick-up . . . . . . . . . . . . 4.12distortion . . . . . . . . . . . . . . . . . . . . . . B.2distortion, amplitude. . 4.23distortion, frequency. . . . . . . . . . . 4.24distortion, phase . . . . . . . . . . . . . . . 4.25distortion, transducer 4.22

distributed system . . . . . . . . . . . . . . . 1.29dominant frequency . . . . . . . . . . 2.13double amplitude (see 2.33)

driving-point impedance. 1.43

driving-point (mechanical) mobility. 1.51duration of shock pulse. . . . . . . . . . 3.18

dynamiccompliance. . . . . (seetable1)dynamicelasticconstant 1.54dynamicspringconstant . . . . . . . . 1.54dynamicstiffness.. . . . . . . . . . . . . . . 1.!54dynamicvibrationabsorber 2.116

E

earth . . . . . . . . . . . . . . . . . . . . . . . . . . B.5earth loop . . . . . . . . . . . . . . . . . . B.7earth wire, . . . . . . . . . . . . . . . . . B.6echo . . . . . . . . . . . . . . . . . . . . . 2.71effective averaging time ., 5.39effective bandwidth . . . . . . 5.36

effective load . . . . . . . . . . . . . . . (see 1.55)effectwe mass . . . . . . . . . . . . . . .,. 1.55effective weight . . . . . . . . . . . . . (see 1.55)eigen mode . . . . . . . . . . . . . . . . . . (see2.55)

electrical noise, . . . . . . . . . . . (see 2.6)electrodynamics vibration generator. 2.92electrodynamics vibration machine. 2.92electromagnetic vibration generator 2.93

30

\ ...—.

IS 11717:2000ISO 2041:1990

electromechanicalpick-up. . . . . . . .ellipticalvibration.. . . . . . . . . . . . . . .ensemble, . . . . . . . . . . . . . . . . . . . . .environment. . . . . . . . . . . . . . . . . . . .equalization(of an electrodynamics

vibrationgeneratorsyatem). . . . .equivalent(atatic)acceleration. . . .equivalentsyatem . . . . . . . . . . . . . . .equivalentviscousdamping. . . . . . .ergodicproceee. . . . . . . . . . . . . . .excitation. . . . . . . . . . . . . . . . . . . . . .excitation,complex. . . . . . . . . . . . . .excitation,shock. . . . . . . . . . . . . . . .excursion. . . . . . . . . . . . . . . . . . . . . .excursion,total . . . . . . . . . . . . . . . . .extraneousvibration. . . . . . . . . . . . .

F

factor,calibration. . . . . . . . . . . . . .. .factor,crest . . . . . . . . . . . . . . . . . ...”factor,form . . . . . . . . . . . . . . . . . . . .FastFourierTransform(FFT}. . . . . .filter. . . . . . . . . . . . . . . . . . . . . . . . . . .filter,band-elimination. . . . . . . . . . .fiker,band-pace. . . . . . . . . . . . . . . . .filter,band-reject. . . . . . . . . . . . . . . .filter,conatant-bandwidth. . . . . . . .filter,cryatal. . . . . . . . . . . . . . . . . . . .filter,high-pass. . . . . . . . . . . . . . . . .filter,low-pass. . . . . . . . . . . . . . . . . .filter,magnetostrictive. . . . . . . . . . .filter,narrow-band . . . . . . . . . . . . . .filter,octave-bandwidth. . . . . . . . . .filter,one-third-octave. . . . . . . . . . .filter,peak-notch. . . . . . . . . . . . . . . .filter,proportional-bandwidth. . . . .fiker,thkd-octave . . . . . . . . . . . . . . .filter,tracking. . . . . . . . . . . . . . . . . . .filter,wave . . . . . . . . . . . . . . . . . . . . .filter,wide-band . . . . . . . . . . . . . . . .finalpeakeewtoothshockpuiaa . . .fixed-baeenaturalfrequency. . . . . .forcedoscillatiorr. . . . . . . . . . . . . . . .forcedvibration. . . . . . . . . . . . . . . . .formfactor . . . . . . . . . . . . . . . . . . . . .foundation. . . . . . . . . . . . . . . . . . . . .Fouriercoefficients. . . . . . . . . . . . . .Fourierintegralequation.. . . . . . . . .Fourierphasespectrum . . . . . . . . . .Fourierseries. . . . . . . . . . . . . . . . . . .Fourierspectrum. . . . . . . . . . . . . . . .Fouriertransform. . . . . . . . . . . . . . . .fractionof criticaldamping.. . . . . . .free impedance. . . . . . . . . . . . . . . .freeoscillation. . . . . . . . . . . . . . . . . .freevibrstion . . . . . . . . . . . . . . . . . . .frequency. . . . . . . . . . . . . . . . . . . . . .frequency-averagedmobility

magnitude . . . . . . . . . . . . . . . . . . .frequency,angular . . . . . . . . . . . . . .frequency,antiresonance.. . . . . . . .frequency,audio . . . . . . . . . . . . . . . .frequency,beat . . . . . . . . . . . . . . . . .frequency,centre . . . . . . . . . . . . . . .frequency,circular . . . . . . . . . . . . . .frequency,cross-over.. . . . . . . . . . .frequency,cut-off . . . . . . . . . . . . . . .frequency,(cyclic). . . . . . . . . . . . . . .frequency,dampednatural . . . . . . .frequencydistortion. . . . . . . . . . . . .

4.2

2.43

5.33

1.11

B.37

5.6

1.25

2.635.31

1.16

1.38

3.3

2.36

2.36

2.20

4.16

2.37

2.36

5,23

B.14

B.32

B.18

B.32

B.21

0.34

B.17B.16

B.35

B.2B

B.27

B.28

6.36

B.22

B.26

6.33

B.14

B.30

3.10

2.76

2.16

2.16

2.36

1.23

A.19

A.20

A.22

A.18

A.21

A.20

2.66

1.45

2.17

2.17

2.24

1.52

2.30

2.752.67

2.29

B.31

2.30

2.106

B .20

2.24

2.81

4.24

frequency, dominant. . . . . . . . . . . . .

frequency, fixed-base natural . . . . .

frequency, fundamental . . . . . . . . . .

frequency, infrasonic . . . . . . . . . . . .

frequency, nominal lower.. . . . . . . .

fraquency, nominal pass-band

centre . . . . . . . . . . . . . . . . . . . . . . .frequency, nominal upper . . . . . . . .

frequency range ofintarest . . . . . . .

frequency, resolution . . . . . . . . . . . .

freauencv resonance. . . . . . . . . . . . .

2.132.762.252.69B.20

B.31B.201.495.122.73

fre&encVresDonse . . . . . . . . . . 4.24: B.13

frequenc~-reiponse function . . . . . .

frequency, sampling . . . . . . . . . . . . .

frequency, ultrasonic . . . . . . . . . . . .

frequency, undamped natural . . . . .function . . . . . . . . . . . . . . . . . . . . . . .

function, cumulative probability

distribution . . . . . . . . . . . . . . . . . . .

function, autocorrelation . . . . . . . . .

function, coherence . . . . . . . . . . . . .

function, crass-correlation . . . . . . . .

function, fraquency-reeponse . . . . .

function, deterministic . . . . . . . . . . .

function, linear . . . . . . . . . . . . . . . . . .

function, probability density . . . . . .

function, probability distribution . . .function. w”ndow . . . . . . . . . . . . . . .

functions, orthogonal . . . . . . . . . . . .fundamental, frequency . . . . . . . . . .

fundamental natural mode of

vibration . . . . . . . . . . . . . . . . . . . . .

fundamental period . . . . . . . . . . . . . .

G

Gaussian distribution . . . . . . . . . . . .

Gaussian random noise.. . . . . . . . . .

generalized coordinates . . . . . . . . . .

geometric mean . . . . . . . . . . . . . . . . .gravity, acceleration of. . . . . . . . . . .

ground . . . . . . . . . . ..> . . . . . . . . . . .

ground loop . . . . . . . . . . . . . . . . . . . .ground wire . . . . . . . . . . . . . . . . . . . .

H

half octave . . . . . . . . . . . . . . . . . . . . .half-sine shock pulse . . . . . . . . . . . . .

harmonic . . . . . . . . . . . . . . . . . . . . . .

haveraine shock pulse. . . . . . . . . . . .

hertz . . . . . . . . . . . . . . . . (eee2.24)I_righ-passfilt er . . . . . . . . . . . . . . . .

hydraulic vibration genarator . . . . . .

I

ideal shock pulsa . . . . . . . . . . . . . . . .

imaginary number . . . . . . . . . . . . .impact . . . . . . . . . . . . . . . . . . . . . . . . .

impedance . . . . . . . . . . . . . . . . . . . . .

impedance, blocked . . . . . . . . . . . . .impedance, direct . . . . . . . . . . . . . . .

impedance, driving-point . . . . . . . . .

impedance, free . . . . . . . . . . . . . . . . .

1.465.15

2.66

2.60A.6

A.34

5.345.4

5.36

1.46

A.26

A.8

A.31

A.34

5.25A.25

2.25

2.60

2.23

A.322.8

A.9

A.36

1.4

B.5

B.7

B.6

B.24

3.9

2.26

3.13

B.17

2.B5

3.8

A.123.5

1.41

1.47

1.43

1.43

1.45

impedance, incremental . . . . . . . (sea 1.41)

impedance, input . . . . . . . . . . . . . . . . B.8impedance, loaded . . . . . . . . . . . . . . 1.46

impedanca; mechanical . . . . . . . . . . 1.42

31

impedance, output . . . . . . . . . . . . . . B.9

impedance, transfer . . . . . . . . . . . . . 1.44

impulse . . . . . . . . . . . . . . . . . . . . . . . . 3.6

incremental impedance. . . . . . . . (see 1.41 )independent variable. . . . . . . . . . . . . A.3

induced environment . . . . . . . . . . . . 1.12

inertia force . . . . . . . . . . . . . . . . . . . . 1.7

inertial force . . . . . . . . . . . . . . . . . . . . 1.7

inertial reference frame. . . . . . . . . . . 1.6

inertial reference system. . . . . . . . . . 1.6

infrasonic . . . . . . . . . . . . . . . . . . . . . . 2.6B

infrasonic frequency . . . . . . . . . . . . . 2.6B

initial peak sewtooth shock pulse . . 3.11

input impedance . . . . . . . . . . . . . . . . B.8

instantaneous value . . . . . . . . . . . . . 2.38

Inverse Fourier transform . . . . . . . . . A.20

inversely proportional. . . . . . . . . . (see A.7)

isolator .. .. . . . . . . . . . . . . . . . . . . . . . .

isolator, shock . . . . . . . . . . . . . . . . . .

isolator, vibration . . . . . . . . . . . . . . . .

J

jerk . . . . . . . . . . . . . . . . . . . . . . . . . . .

L

level . . . . . . . . . . . . . . . . . . . . . . . . . . .Iirreapectrum . . . . . . . . . . . . . . . . . . .

Iirrearfunction . . . . . . . . . . . . . . . . . .Iinearaweep rate . . . . . . . . . . . . . . . .

Iinearsyatem . . . . . . . . . . . . . . . . . . .

Iineertransducer . . . . . . . . . . . . . . . .

Iinearvibretion . . . . . . . . . . . . . . . . . .

linear viscous damping . . . . . . . . . . .

linear viscous damping coefficient .

Ioadedimpedance . . . . . . . . . . . . . . .

logarithmic decrement . . . . . . . . . . .

logarithmic frequency sweep rate . .

longitudinal wave . . . . . . . . . . . . . . .

loop . . . . . . . . . . . . . . . . . . . . . . . . . . .

Iow-pass filter . . . . . . . . . . . . . . . . . . .

Iumped mass . . . . . . . . . . . . . . . . . . .

M

mechlne, electrodynamics vibration .mschine, vibration . . . . . . . . . . . . . . .

msgnetostrictive filter. . . . . . . . . . . .

magnetostrictive vibration

generator . . . . . . . . . . . . . . . . . . . .magnitude, peak . . . . . . . . . . . . . . . .

mass, apparent . . . . . . . . . . . . . . . . .maes, effective . . . . . . . . . . . . . . . . . .

ins&, lumped . . . . . . . . . . . . . . . . . . .

masa, pure . . . . . . . . . . . . . . . . . . . :.

maxima . . . . . . . . . . . . . . . . . . . . . . .

maximum value . . . . . . . . . . . . . . . . .

mean, arithmetic . . . . . . . . . . . . . . . .

mean, geometric . . . . . . . . . . . . . . . .

mean-equarevalue . . . . . . . . . . . . . .

meanvalue . . . . . . . . . . . . . . . . . . . . .

2.109

2.111

2.110

1.5

1.57

A.23

A.8

2.1061.21

4.4

2.44

2.62

2.641.46

2.67

2.107

2.60

2.47

B.16

2.lCKI

2.92

2.90

8.35

2.BB

2.34

1.651.56

2.100

2.1002.41

2.40

A.35

A.36

A.40

A.35

mechanical admittance . . . . . . (see table 1)mechanical direct-drive vibration

generator . . . . . . . . . . . . . . . . . . . . 2.94

mechanical impedance . . . . . . . . . . . 1.42

mechanical mobility . . . . . . . . . . . . . 1.50

mechanical reaction typa vibration

generator . . . . . . . . . . . . . . . . . . . . 2.96

Is 11717:2000ISO 2041:1990

mechanical shock . . . . . . . . . . . . . .

mechanical system . . . . . . . . . . . . . .

mobility, (mechanical) . . . . . . . . . . .

mobility, direct (mechanical) . . . . . .

mobility, driving-point (mechanical)

mobility magnitude, fraquency-

averaged . . . . . . . . . . . . . . . . . . . .

mobility, mechanical . . . . . . . . . . . . .

mobility, transfer (mechanical) . . . .modal numbers . . . . . . . . . . . .

3.1

1.22

1.50

1.51

1.51

1.52

1.50

1.53

2.52

mode, characteristic . . . . . . . (see 2.55)mode, eigen . . . . . . . . . . . . . . . . . (see2.55)

mode, natural . . . . . . . . . . . . . . . . (see2.55)

moda, normal . . . . . . . . . . . . . . . 2.55

mode of vibration . . . . . . . . . . . . . . . 2.46mode of vibration, natural . . . . . . . . 2.49mode of vibration, fundamental

natural . . . . . . . . . . . . . . . . . . . . . . . 2.50

mode, shape . . . . . . . . . . . . . . . . . . . 2.51

modes, coupled . . . . . . . . . . . . . . . . . 2.53

modes, uncoupled . . . . . . . . . . . . . . . 2.54

modulus . . . . . . . . . . . . . . . . . . . . . . . A.16

motion, aperiodic . . . . . . . . . . . . . . . 2.21

motion, shock . . . . . . . . . . . . . . . . . . 3.4moving element . . . . . . . . . . . . . (see 2.92)multi-degree-of-freedom system . . . 1.28

multi-sinusoidal vibration . . . . . . (see 2.3)

N

narrow-band filter . . . . . . . . . . . . . . . B.29narrow-band random vibration . . . . 2.11natural environment . . . . . . . . . . . . . 1.13natural frequency, damped . . . . . . . 2.81natural frequency, fixed-base . . . . . 2.76natural frequency, undamped . . . . . 2.60

natural mode . . . . . . . . . . . . . . . . (see 2.55)natural mode of vibration . . . . . . . . . 2.48

natural mode of vibration,

fundamental . . . . . . . . . . . . . . . . . . 2.50

negative peak value . . . . . . . . . . . . . . 2.34neutral axis . . . . . . . . . . . . . . . . . . . . . 1.38neutral surf ace . . . . . . . . . . . . . . . . . 1.35node . . . . . . . . . . . . . . . . . . . . . . . . . . 2.46noise . . . . . . . . . . . . . . . . . . . . . . . . . 2.6noisa, acoustic . . . . . . . . . . . . . . . (see 2.6)noise, electrical ., . . . . . . . . . . . . . (see 2.6)

noise, Gaussian random ., . . . . . . . . 2.8noiae, pink . . . . . . . . . . . . . . . . . . . . . 2.10noiaa, random . . . . . . . . . . . . . . . . . 2.7noise, white . . . . . . . . . . . . . . . . . . . . 2.9nominal bandwidth . . . . . . . . . . . . . . B.19nominal lower cut-off frequency . . . B.20nominal pass-band centre frequency B.31nominal pulse . . . . . . . . . . . . . . . . . . . 3.16nominal shock pulsa. . . . . . . . . . . . . 3.16nominal upper cut-off frequency. . . B.20nominal value of a shock pulse . . . . 3.17non-linear damping . . . . . . . . . . . . . . 2.86

non-stationary vibration . . . . . . . . 2.5,5.32normal distribution . . . . . . . . . . . . . . A.32normal mode . . . . . . . . . . . . . . . . . . . 2.55normal probability density distribution A.32numbers, modal . . . . . . . . . . . . . . . . . 2.52

0octave . . . . . . . . . . . . . . . . . . . . . . . . . B.23octave-bandwidth filter. . . . . . . . . . . B.27one-half octave . . . . . . . . . . . . . . . . . B.24

one-tenth decade . . . . . . . . . . . . . . .

one-third octave . . . . . . . . . . . . . . . .

one-third-octave filter . . . . . . . . . . . .

operational amplifier . . . . . . . . . . . . .

orthogonal functions. . . . . . . . . . . . .

oscillatio n. . . . . . . . . . . . . . . . . . . . .

oscillation, forced . . . . . . . . . . . . . .

oscillation, free . . . . . . . . . . . . . . . . .

output impedance . . . . . . . . . . . . . . .

overshoot . . . . . . . . . . . . . . . . . . . . . .

B.26

B.25

B.2B

B.1O

A.25

1.82.16

2.17

B.91.19

overtone . . . . . . . . . . . . . . . . . . . . (see 2.26)

P

parameter . . . . . . . . . . . . . . . . . . . . . . A.5pass-band . . . . . . . . . . . . . . . . . . . . . . B.15peak amplitude. . . . . . . . . . . . . . . (see 2.33)peak magnitude . . . . . . . . . . . . . . . . . 2.34peak-notch filter . . . . . . . . . . . . . . . . B.36peak-to-peak value . . . . . . . . . . . . . . 2.35peak-to-r.m.s. ratio . . . . . . . . . . . . . . 2.37peakvalue . . . . . . . . . . . . . . . . . . . . . 2.34peak value, negative . . . . . . . . . . . . . 2.34peak value, positive. . . . . . . . . . . . . . 2.34period . . . . . . . . . . . . . . . . . . . . . . . . . 2.23period, cycle . . . . . . . . . . . . . . . . . . . . 2.102period, fundamental . . . ... . . . . . . . . 2.23periodic vibration . . . . . . . . . . . . . . . . 2.2Deriodic ouantitv . . . . . . . . . . . . . . (see 2.2)phase . .”. . . . . .’. . . . . . . . . . . . . . . . .phase angle . . . . . . . . . . . . . . . . . . . .phase angle difference . . . . . . . . . . .

phaee difference . . . . . . . . . . . . . . . .

phase distortion . . . . . . . . . . . . . . . .

phase shift, transducer . . . . . . . . .

phase spectrum . . . . . . . . . . . . . . . . .

phasor . . . . . . . . . . . . . . . . . . . . . . . . .

pick-up, acceleration. . . . . . . . . . . . .

pick-up, displacement. . . . . . . . . . . .

pick-up, electromechanical . . . . . . .

pick-up, seismic . . . . . . . . . . . . . . .

pick-up, velocity . . . . . . . . . . . . . . . .

piezoelectric vibration generator .

pinknoise . . . . . . . . . . . . . . . . . . . . . .

pink random vibration . . . . . . . . . . . .

plane wave.........,........,..

positive peakvalue . . . . . . . . . . . . . .

power spectral density . . . . . . . . . . .

power spectrum . . . . . . . . . . . . . . . . .preconditioning . . . . . . . . . . . . . . . . .

principal axes of inertia . . . . . . . . . . .

2,312.312.32

2.32

4.25

4.21

A.22

A.144.10

4.12

4.2

4.3

4.11

2.86

2.10

2.10

2.64

2.34

5.1

5.21.14

1.32

mincioal moments of inertia . . . . (see 1.32)probability. . . . . . . . . . . . . . . . . . . . .

probability densrty . . . . . . . . . . . . . .

probability density distribution curve

@obability density distribution,

normal . . . . . . . . . . . . . . . . . . . . . . .probability density function . . . . . . .

probability distribution function.

probability distribution function,

cumulative . . . . . . . . . . . . . . . . . . .process . . . . . . . . . . . . . . . . . . . . . . . .

process, ergodic . . . . . . . . . . . . . . . .

process, random . . . . . . . . . . . . . . . .

process, stationary . . . . . . . . . . . . . .

process, stochastic . . . . . . . . . . . . . .

proportional . . . . . . . . . . . . . . . . . . . .

proportional-bandwidth filter. . . . . .

pseudovelocity . . . . . . . . . . . . . . . . . .

pulaa decay time . . . . . . . . . . . . . . . .

pulaedrop-off time . . . . . . . . . . . . . .

pulse, duration of shock . . . . . . . . . .

32

A.28

A.30

A.31

A.32

A.31

A.34

A.34

A.28

5.31

5.32

5.26

5.32

A.7

B.22

5.7

3.20

3.203.18

pulse, final peak sawtooth shock. . .

pulse, half-sine shock . . . . . . . . . . . .

pulse, haversine shock . . . . . . . . . . .

pulaa, ideal shock . . . . . . . . . . . . . . .

pulse, initial peak sawtooth shock. .

pulse, nominal . . . . . . . . . . . . . . . . . .

pulse, nominal shock . . . . . . . . . . . .

pulse, nominal value of a shock. . . .pulse, rectangular shock . . . . . . . . . .

pulse risetime . . . . . . . . . . . . . . . . . .

pulaa, shock . . . . . . . . . . . . . . . . . . . .

pulse, symmetrical triangular shock

pulse, terminal peak sawtooth

shock . . . . . . . . . . . . . . . . . . . . . . .pulse, trapezoidal shock . . . . . . . . . .

puisa, versine shock . . . . . . . . . . . . .

pure mass . . . . . . . . . . . . . . . . . . . . .

Q

Q; Q factor . . . . . . . . . . . . . . . . . . . .

quantizing . . . . . . . . . . . . . . . . . . . . .

3.10

3.9

3.133.8

3.11

3.16

3.16

3.17

3.14

3.19

3.2

3.12

3.10

3.15

3.13

2.100

2.88

5.24quasi-per~dic vibration. . . . . . . . . (see 2.2)

quasi-sinusoidal vibration . . . . . . . (see 2.3)

R

random noiaa . . . . . . . . . . . . . . . . . . .

random noise, Gaussian . . . . . . . . . .

random process . . . . . . . . . . . . . . . . .

random vibration . . . . . . . . . . . . . . . .

random vibration, broad-band . . . . .

random vibration, narrow-band. . . .

random vibration, pink . . . . . . . . . . .

random vibration, white . . . . . . . . .

ratio, cross-sensitivity. . . . . . . . . . . .

ratio, damping . . . . . . . . . . . . . .

ratio, peak-to-r. m.s. . . . . . . . . . . .

ratio, transverse sensitivy. . . . . . . . .

Rayleigh distribution . . . . . . . . . . . . .real-time analysis . . . . . . . . . . .

;:,,

2.7

2.8

5.322.4

2.12

2.11

2.10

2.9

4.20

2.86

2.37

4.20

A.33

5.22

receptance. . . . . . . . . . . . . . . . (aeetablel)rectangular shock pulse . . . . . . . . . 3.14rectilinear transducer . . . . . . . . . . . . 4.8rectilinear vibration . . . . . . . . . . . . . 2.44reference . . . . . . . . . . . . . . . . . A.1reference, common . . . . . . . . . . . (see Al)

relative displacement . . . . . . . . . . . .

relative velocity . . . . . . . . . . . . . .

relaxation time . . . . . . . . . . . . . . . . . .

resolution . . . . . . . . . . . . . . . . . . . .

resonance . . . . . . . . . . . . . . . . . . . . . .

resonance frequency. . . . . . . . . . . . .

resonance response, subharmonic .

resonance vibration generator . . . . .

response . . . . . . . . . . . . . . . . . . . . . . .

response, complex . . . . . . . . . . . . . .

response, frequency . . . . . . . . . . . . .

reaponae function, frequency . . . . .

response spectrum, shock . . . . . . . .

response, subharmonic . . . . . . . . . .

response, subharmonic resonance

reverberation . . . . . . . . . . . . . . . . . . .

riaa time . . . . . . . . . . . . . . . . . . . . . .

riaatime, pulaa . . . . . . . . . . . . . . . . .

r.m. s. value . . . . . . . . . . . . . . . . . . . .

root-mean-square value . . . . . . . . . .

1.11.2

B.4

B.3

2.72

2.73

2.78

2.97

1.17

1.39

4.24

1.48

3.24

2.78

2.78

2.70

3.193.19

A.37

A.37

\ ...—.—. __ _____ . -—-

Is 11717:2000ISO 2041:1990

s

sample (verb) . . . . . . . . . . . . . . . . . . .

sampling . . . . . . . . . . . . . . . . . . . . .

aampling frequency . . . . . . . . . . . . .

eempling interval . . . . . . . . . . . . .

scalar . . . . . . . . . . . . . . . . . . . . . . . . . .

seismic pick-up . . . . . . . . . . . . . . . . .

Seiamic system . . . . . . . . . . . . . . . . .

self-excited vibration. . . . . . . . . . . . .

self-induced vibrstion . . . . . . . . . . . .

self-stationary, strongly . . . . . . . . . .

self-stationary, weakly . . . . . . . . . . .

Sansing element . . . . . . . . . . . . . . . . .

sensitive axis . . . . . . . . . . . . . . . . . . .sensitivity . . . . . . . . . . . . . . . . . . . . . .

sensitivity ratio, transverse. . . . . . . .

sensitivity, transverse . . . . . . . . . . . .

set . . . . . . . . . . . . . . . . . . . . . . . . . . . .

severity, vibration . . . . . . . . . . . . . . .ehape, mode . . . . . . . . . . . . . . . . . . .

Strearwav e. . . . . . . . . . . . . . . . . . . .

shock . . . . . . . . . . . . . . . . . . . . . . . . .

shock abaorber . . . . . . . . . . . . . . . . .

shock, applied . . . . . . . . . . . . . . . . . .

shock, excitation . . . . . . . . . . . . . . . .$hockiaolator . . . . . . . . . . . . . . . . . . .

shock machine . . . . . . . . . . . . . . . . . .

shock, mechanical . . . . . . . . . . . . . . .

shock motion . . . . . . . . . . . . . . . . . . .

shock pulsa . . . . . . . . . . . . . . . . . . . .

shock pulse, duration of . . . . . . . . . .

shock pulse, final peak sawtooth. . .

shock puls@~half-sine . . . . . . . . . . . .

shock pulse, haversine . . . . . . . . . . .

shock pulee, ideal . . . . . . . . . . . . . . .

shock pulse, initial peak sawtooth.

shock pulsa, nominal . . . . . . . . . . . .

shock pulse, nominal value of a . . . .

shock pulse, rectangular. . . . . . . . . .ishock pulse, symmetrical triangular

shock pulse, terminal peakSawtooth . . . . . . . . . . . . . . . . . . . .

shock pulse, trapezoidal . . . . . . . . . .ehockpulae, versine . . . . . . . . . . . . .

shock response spectrum. . . . . . . . .

shock testing machine . . . . . . . . . . .shock wave . . . . . . . . . . . . . . . . . . . .signal . . . . . . . . . . . . . . . . . . . . . . . . . .

simple harmonic vibration . . . . . . . .

5.14

5.14

5.15

5.16

All

4.3

1.24

2.18

2.18

5.28

5.30

4.7

4.17

4.15

4.20

4.19

5.33

2.42

2.51

2.61

3.12.113

3.3

3.32.111

3.23

3.1

3.4

3.2

3.18

3.10

3.9

3.13

3.8

3.11

3.16

3.17

3.14

3.12

3.103.15

3.13

3.24

3.23

3.22

8.1

2.3single amplitude . . . . . . . . . . . . . . (sea 2.33)single degree-of-freedom system . 1.27sinusoidal vibration . . . . . . . . . . . . . . 2.3smoothing . . . . . . . . . . . . . . . . . . . . . 5.17snubber . . . . . . . . . . . . . . . . . . . . . . . . 2.115sound . . . . . . . . . . . . . . . . . . . . . . . . . 1.9spectrum density, acceleration . . (see 5.1 )spectrum density, acceleration

power . . . . . . . . . . . . . . . . . . . . . (see 5.1 )spectral density, power. . . . . . . . . . . 5.1Spectrum . . . . . . . . . . . . . . . . . . . . . . 1.56spectrum, continuous. . . . . . . . . . . . A.24spectrum, Fourier . . . . . . . . . . . A.21spectrum, Fourier phase. . . . . . . . . . A.22

spectrum, line . . . . . . . . . . . . . . . . . . A.23spectrum, phase . . . . . . . . . . . . . . . . A.22spectrum, power . . . . . . . . . . ... . . . . 5.2spectrum, shock response . . . . . . . . 3.24epeed, critical . . . . . . . . . . . . . . . . . . . 2.77spherical wave . . . . . . . . . . . . . . . . . . 2.65standard deviation . . . . . . . . . . . . . . . A.36

standing wave . . . . . . . . . . . . . . . . . .

stationary proceaa . . . . . . . . . . . . . . .

statistical degrees of freedom . . . . .steady-state vibration . . . . . . . . . . . .

stiffness . . . . . . . . . . . . . . . . . . . . . . .stiffness, dynamic . . . . . . . . . . . . . . .

stimulus . . . . . . . . . . . . . . . . . . . . . . .

etochaatic procesa . . . . . . . . . . . . . . .

strongly self-stationary . . . . . . . . . . .

subharmonic . . . . . . . . . . . . . . . . . . .

subharmonic resonance response. .

subharmonic response . . . . . . . . . . .

superposition principle . . . . . . . . . . .

sweep . . . . . . . . . . . . . . . . . . . . . . . . .sweep rate . . . . . . . . . . . . . . . . . . . . .

svmep rate, linear . . . . . . . . . . . . . . .swap rate, uniform . . . . . . . . . . . . .

sweep rate, Iogariihmic frequency .symmetricaltriangularshockpulse.system . . . . . . . . . . . . . . . . . . . . . . . .syatam,continuous. . . . . . . . . . . . . .ayatem,distributed. . . . . . . . . . . . . .syatam,equivalent . . . . . . . . . . . . . .systam,linear. . . . . . . . . . . . . . . . . . .system,mechanical.. . . . . . . . . . . . .system,multi-degrea-of-freedom. .systam,seiamic. . . . . . . . . . . . . . . . .system, single degree-of-freedom. .

system, vibration generator . . . . . . .

T

terminal peak sawtooth shock pulse

third octave . . . . . . . . . . . . . . . . . . . .

third-octave filter . . . . . . . . . . . . . . . .

time constant . . . . . . . . . . . . . . . . . . .

time history . . . . . . . . . . . . . . . . . . . .total excursion . . . . . . . . . . . . . . . . . .

total time (in data processing) . . . . .

tracking filter . . . . . . . . . . . . . . . . . . .

transducer . . . . . . . . . . . . . . . . . . . . .

transducer, angular, . . . . . . . . . . . . .

transducer, bilateral . . . . . . . . . . . . .

transducer distortion. . . . . . . . . . . . .

transducer, linear . . . . . . . . . . . . . . . .

transducer, phase shift . . . . . . . . . . .tranaducar, rectilinear. . . . . . . . . . . .

transducer, unilateral . . . . . . . . . . . .

tranaferfunction . . . . . . . . . . . . . . . .

trh,wfer impedance . . . . . . . . . . . . . .

transfer (mechanical) mobility . . . . .

transient vibration . . . . . . . . . . . . . . .

tranamiaaibility . . . . . . . . . . . . . . . . . .

tranaveraa axis . . . . . . . . . . . . . . . . . .

transverse sensitivity. . . . . . . . . . . . .

transverse aenaitivity ratio . . . . . . . .tranavaraa wave . . . . . . . . . . . . . . . . .

trapezoidal shock pulse. . . . . . . . . . .

truncation . . . . . . . . . . . . . . . . . . . . . .

uultrasonic . . . . . . . . . . . . . . . . . . . . . .

ultrasonic frequency . . . . . . . . . . . . .

unbalanced mass vibration generatoruncoupled modes . . . . . . . . . . . . . . .

undamped natural frequency. . . . . .

undershoot . . . . . . . . . . . . . . . . . .

underwater blast . . . . . . . . . . . . . . . .

uniform swaep rate . . . . . . . . . . . . . .

unilateral transducer . . . . . . . . . . . . .

33

2.665.265.5

2.141.331.541.16

5.32

5.28

2.27

2.76

2.76

A.27

2.104

2.105

2.lm

2.106

2.107

3.121.20

1.28

1.28

1.25

1.21

1.22

1.26

1.24

1.27

2.91

3.10

B.25

B.26

B.4

5.27

2.36

5.13

B.33

4.1

4.9

4.6

4.22

4.4

4.21

4.8

4.51.37

1.44

1.53

2.15

1.18

4.18

4,19

4.20

2.62

3.15

5.18

2.66

2.66

2.86

2.54

2.60

1.19

3.21

2.106

4.5

v

vacua . . . . . . . . . . . . . . . . . . . . . . . . . .

valua, absolute, . . . . . . . . . . . .,’ . . . .

value, inetantanaous. . . . . . . . . . . . .

value, maximum . . . . . . . . . . . . . . . .

vakra, maan-aquara, . . . . . . . . . . . . .

valua, paak . . . . . . . . . . . . . . . . . . . . .

value, peak-to-peak. . . . . . . . . . . . . .

valua, r.m.s . . . . . . . . . . . . . . . . . . . . .

value, root-mean-equara . . . . . . . . .

variable . . . . . . . . . . . . . . . . . . . . . . . .

variable, dapandent . . . . . . . . . . . . . .

variable, independent . . . . . . . . . . . .

variance . . . . . . . . . . . . . . . . . . . . . . .

vector . . . . . . . . . . . . . . . . . . . . . . . . .

2.39

A.17

2.38

2.40

A.40

2.34

2.35

A.37

A.37

A.2

A.4

A.3

A.38

A.1Ovactoramplitude . . . . . . . . . . . . . (See 2.33)velocity . . . . . . . . . . . . . . . . . . . . . . . .

velocity pick-up . . . . . . . . . . . . . . . . .

versinaehock pulse . . . . . . . . . . . . . .

vibration . . . . . . . . . . . . . . . . . . . . . . .

vibration absorber, dygamic. . . . . . .

vibration, ambient . . . . . . . . . . . . . . .

vibration, broad-band random. . . . .

vibration, circular. . . . . . . . . . . . . . . .

vibration, daterminiatic . . . . . . . . . . .

vibration, elliptical . . . . . . . . . . . . . . .

vibration, axtranaous . . . . . . . . . . . .vibration, forced . . . . . . . . . . . . . . . .vibration, free . . . . . . . . . . . . . . . . . . .

vibration, fundamental natural

modeof . . . . . . . . . . . . . . . . . . . . .vibration generator . . . . . . . . . . . . . .

vibration generator, direct-drive . . .

vibration generator, alectrodynamic

vibration generator,

elactromagnatic . . . . . . . . . . . . . . .

vibration generator, hydraulic . . . . .

vibration generator,

magnatostrictive . . . . . . . . . . . . . .

vibration ganerator, mechanical

direct-drive . . . . . . . . . . . . . . . . . . .

vibration generator, mechanical

reaction type . . . . . . . . . . . . . . . . .vibration ganerator, piazoelectric . .

vibration ganerator, resonant . . . . . .vibration ganerator system. . . . . . . .

vibration generator, unbalanced

mass . . . . . . . . . . . . . . . . . . . . . . . .vibration isolator . . . . . . . . . . . . . . . .vibration, linear . . . . . . . . . . . . . . . . .

vibration machine . . . . . . . . . . . . . . .

vibration machina, electrodynamics .

vibration, modeof . . . . . . . . . . . . . . .

vibration, narrow-band random. . . .

vibration, natural mode of . . . . . . . .

vibration, non-stationary . . . . . . . .vibration, periodic . . . . . . . . . . . . . . .

vibration, pink random . . . . . . . . . . .

vibration, random . . . . . . . . . . . . . . .vibration, rectilinear . . . . . . . . . . . . .

vibration, self-excited . . . . . . . . . . . .

vibration, self-induced . . . . . .. . . . . .

vibration severity . . . . . . . . . . . . . . . .

vibration, simple harmonic. . . . . . . .

vibration, sinusoidal . . . . . . . . . . . . .

vibration, steady-state . . . . . . . . . . .vibration, transient . . . . . . . . . . . . . .

vibration, white random . . . . . . . . . .

vibrograph . . . . . . . . . . . . . . . . . . . . .

vibrometer . . . . . . . . . . . . . . . . . . . . .

1.024.113.132.1

2.1162.192.122.455.262.432.202.162.17

2.502.%2.842.92

2.832.95

2.88

2.84

2.%2.862.972.91

2.862.1102.442.802.922.462.112.482.52.2

2.102.4

2.442.162.182.422.32.3

2.142.152.9

4.134.14

IS 11717:2000ISO 2041:1990

viscous damping . . . . . . . . . . . . . . . .viscous damping coefficient . . . . . . .viscous damping coefficient, linear.viscous damping, critical . . . . . . . . .viscous damping, equivalent . . . . . .viacous damping, linear . . . . . . . . . .

wwave . . . . . . . . . . . . . . . . . . . . . . .

2.622.64

%2.832.62

2.%

wave, compressional . . . . . . . . . . . .

wave filter . . . . . . . . . . . . . . . . . . . . . .

wave front . . . . . . . . . . . . . . . . . . . . .

wave, longitudinal . . . . . . . . . . . . . . .

wave, plane . . . . . . . . . . . . . . . . . .

wave, shear . . . . . . . . . . . . . . . . . . . .

wave~ shock . . . . . . . . . . . . . . . . . . . .

wave, spherical . . . . . . . . . . . . . . . . .

2.59

B.14

2.63

2.60

2.&l

2.61

3.22

2.66

wave, standing . . . . . . . . . . . . . . . . .

wavetrain . . . . . . . . . . . . . . . . . . . . . .

wave, transver.s.e . . . . . . . . . . . . . . . .

wavelength . . . . . . . . . . . . . . . . . . . . .

weakly self-stationary . . . . . . . . . . . .

white noise . . . . . . . . . . . . . . . . . . . . .

white random vibration. . . . . . . . . . .

wide-band filter . . . . . . . . . . . . . . . . .

window function . . . . . . . . . . . . . . . .

2.=

2.57

2.62

2.56

5.302.9

2.9

B.30

5.25

34

Bureau of Indian Standards

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Amendments Issued Since Publication

Amend No. Date of Issue Text Affected

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