msc nastran random dynamics

Visteon Visteon October 2004, October 2004, Page 1--11

Random Response Analysis

Visteon Visteon October 2004, Page 1October 2004, Page 1--22

Dynamic Environments

• Harmonic, periodic and nonperiodic (transient)

• Predictable at any time t using a function

• No harmonic component• Cannot be predictable at any

time t using a function.

Random

Stationary Nonstationary

Ergodic

Deterministic

Periodic Transient

SimpleHarmonic

ShockSpectra

SOL 108/111

SOL 109/112

SOL 103


Concepts• Statistical (only method to describe random events)

• Mean (average) statistic• Variability statistic

• Variance and standard deviation• Time and Frequency Relation

• Fourier transform• Decomposes or separates a waveform or function into sinusoids of

different frequency which sum to the original waveform.• Equations used for simple functions• FFT algorithms for complex time measurements

• Frequency spectrums• Power for energy content• Density for distribution of power over the spectrum

• Units• Most common source of questions and errors


Statistic Basics

• Mean (average) This section is not intended as a complete description of statistical theory. Presented is the basics along with a physical interpretation that lays the ground work for MSC.Nastran Random analysis.

points data of number total #ki datapoint individualX

AverageXk

XX

i

k

1ii

===

=∑=

•Example - Gridpoint stress average• Total number of elements connected to the gridpoint = k• Datapoint i is the gridpoint σy stress from each element


Statistic Basics cont

• Mean Square Value

( )

points data of number total ki datapoint individualX

Square eanMk

X

i

2

k

1i

2i

2

===

=∑=

ψ

ψ The square root of Mean Square is the Root Mean Square (RMS). The RMS is used to measure power.



• Variance

( )

points data of number total ki datapoint individualX

AverageX

Variances1k

XXs

i

2

k

1i

2

i2

===

=−

−=∑=

Standard Deviation

Deviation Standardsss 2

==



• Correlation• Measure the strength of the relationship between two variables

• Autocorrelation is used in random response• Scatter plots for visual review (examples to follow)• Perfect correlation implies a mathematical relationship• Error measurements evaluate the correlation

• Linear• nonlinear

( )

( )( )

rrorE

yxf

xfyk

1i

2ii

=

−=

=

∑=

ε

εCorrelation is used to judge if an event is random or deterministic.



• Correlation – graphical example

-1.0

-0.5

0.0

0.5

1.0

-1.0 -0.5 0.0 0.5 1.0

sin(t)

sin(

t+ta

u)

tau=0.0

-1.0

-0.5

0.0

0.5

1.0

-1.0 -0.5 0.0 0.5 1.0

sin(t)

sin(

t+ta

u)

tau=0.3

The plots indicate a correlation between sin(t) and sin(t+τ). Thus the sin function is not random.

-1.0

-0.5

0.0

0.5

1.0

-1.0 -0.5 0.0 0.5 1.0

sin(t)

sin(

t+ta

u)

tau=0.6

-1.0

-0.5

0.0

0.5

1.0

-1.0 -0.5 0.0 0.5 1.0

sin(t)

sin(

t+ta

u)

tau=3.0



• Correlation – graphical examplet au=0.0

4.8

5

5.2

5.4

5.6

5.8

6

6.2

4.8 5 5.2 5.4 5.6 5.8 6 6.2

s i g n a l ( t )

t a u=0.0t a u=0.3

4.8

5

5.2

5.4

5.6

5.8

6

6.2

4.8 5 5.2 5.4 5.6 5.8 6 6.2

s i g n a l ( t )

t a u=0.3

Random signals produce scatter plots for any value of τ that is NOT 0.0. Thus the measured data only correlates with itself when τ is 0.0.

t a u=1.0

4.8

5

5.2

5.4

5.6

5.8

6

6.2

4.8 5 5.2 5.4 5.6 5.8 6 6.2

s i g n a l ( t )

t a u=1.0

t a u=3.0

4.8

5

5.2

5.4

5.6

5.8

6

6.2

4.8 5 5.2 5.4 5.6 5.8 6 6.2

s i g n a l ( t )

t a u=3.0



• Averages for time measured responses• Ensemble (points from all tests) and Temporal (points in only one test)• Apply to deterministic and random responses

Measured Output at Location 10

4.8

5.0

5.2

5.4

5.6

5.8

6.0

6.2

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010Time (seconds)

Acc

eler

atio

n (m

m/s

ec/s

ec)

Test 1Test 2Test 3Test 4

The variable time is now introduced



Temporal Averaging

Ense

mbl

e A

vera

ging

t1

τ

Which single test is representative of the response?

Statistical properties provide an answer.

Note t1 and τ asthey are used in the statistical equations that follow



• Ensemble average• Averages using single data points from each test

( )( )

( )

( )1)k (unless u

t at responses (i) test Individualtutests of number Totalk

ttime at response Averagetk

tut

11i

11

k

1i1i

1

=≠=

==

=∑=

µ

µ

µEnsemble average or mean value. In general the average changes with respect to the selected t1.

( )( )

k

tulimt

k

1i1i

j1

∑=

∞→=µ General expression (note the ‘bar’ in the

original expression X is implied by µ)



• Ensemble average• Averages using multiple data points from each test

• 3 examples but not limited to these equations

( )( ) ( )

k

tutulimt,tR

k

1i1i1i

k11u

∑=

∞→

−=−

ττ

This average is called the Autocorrelation Function and in general changes with respect to the selected t1

( )( ) ( ) ( )

k

tututulimt,t,tR

k

1i1i1i1i

k111u

∑=

∞→

−−=−−

στστ

( )( ) ( ) ( ) ( )

k

tutututulimt,t,t,tR

k

1i1i1i1i1i

k1111u

∑=

∞→

−−−=−−−

βστβστ

Rar

ely

used



• Ensemble average• Nonstationary means:

( )( )

k

tulimt

k

1i1i

j1

∑=

∞→=µ( )

( ) 111u

11

t withvariable is t,tRand

t withvariable is t

τ

µ

+

Stationary means:

( )

( ) 111u

11

t valueany for constant t,tRand

t valueany for constantt

=+

=

τ

µ The strength of the stationary property increases when the higher order averages (3 or more data points per test) also become constant for any t1. Most physical responses can be assumed to be strongly stationary when the average and autocorrelation values are constant with any t1.

The Autocorrelation Function does change when τ is changed.



• Temporal average• Averages based on one test Note that time averages

require integration and the test selected is ‘j’ among the ‘k’ number tests available for selection

( ) ( )∫−∞→=

2T

2T jTdttu

T1limjµ

( ) ( ) ( )dttutuT1lim,tR

2T

2T jjTu ∫−∞→−= ττ

Temporal Autocorrelation Function. (There are higher order integrations available similar to the ensemble examples.)•Ergodic means:

( ) constk == µµ For any test ‘j’ among the ‘k’ number of tests in the ensemble, the average is the same.

( ) ( )ττ R,kR =



• Ergodic

The strength of the ergodic property increases with when the higher order averages (3 or more data points per integration) also become constant for any τ, σ, β, ….. Most physical responses can be assumed to be strongly ergodic when the average and autocorrelation values are constant with any τ..

Basic assumption for random responses:

With stationary and ergodic established for a response, only one measurement is needed to represent the response. The statistical properties are the same for all measurements.


Time Based Example• Temporal Mean (average)

A

0-T T-T

2T2

3T2

A

( )4Adtt

TA2

T1 2T

2T== ∫−µ

0-T2

T2

A4


Time Based Example cont

• Temporal Autocorrelation Function

0<τ<T/2

( ) ( ) dttTA2t

TA2

T1R

2T

0∫−

+=τ

ττ

( ) ( )( )dtTtTA2t

TA2

T1R

2T

T∫ −−−=

τττ

T/2<τ<T A

0-T T-T

2T2

3T2

A

0-T T-T

2T2

3T2

τ

τ

We are calculating the overlapping areas shown by the grey vertical lines to get the ‘correlation’ of the function vs τ not the area. Two integration functions needed depending on τ and the period T.



• Temporal Autocorrelation Function• R(τ) is periodic • Deterministic functions produce periodic correlation functions

R(τ)

τ0



• Temporal Autocorrelation Function• Random functions generate autocorrelation that only has a

nonzero value when τ is 0 (see previous scatter plots)

R(τ) Note the mean square (ψ2) is equal to the autocorrelation (R(τ)) when τ is 0.

τ0



• Cross Correlation Function• Calculating the correlation between two measurements taken at

different locations• Same location is autocorrelation

• Examples of use• Verification of a specific signal in a noisy data measurement• Tracking graphic features in animations• Matching tests

• Automotive – road input• Commonality between left and right tire inputs

( ) ( ) ( )dttutuT1limR

2T

2T 21T2u,1u ∫−∞→−= ττ

http://www.umtri.umich.edu/erd/roughness/irrpd.pdf



• Time based analysis in MSC.Nastran• Requires the time vs value points of the function• Each measurement of the ensemble will produce a different result• Number of Nastran solutions = Number of measured test data

records• Which one do you use?

• Random functions have constant averages• Mean• Autocorrelation

• MSC.Nastran does not have a method to apply these single average values in the time domain.

• Move to the analysis to the frequency domain• Random signal statistical properties change with frequency

• The stationary and ergodic properties still hold


Frequency Domain

• The time based equations for averages and correlation have equivalents in the frequency domain.

• Averages using multiple data points from each test• Averages based on one test

• Stationary and Ergodic properties are equivalent• Changing domains does not change the properties of the data• One test can be used to represent all tests when

• Stationary established• Ergodic established

• Need to define the frequency equivalents • We only need the autocorrelation for random


Frequency Domain cont

• Simple Fourier conversions• Period functions can be represented in frequency using

• The work is finding the• A terms• B terms• ω values

( ) ∑=

+=n

1kkkkk t2sinBt2cosAtu πωπω



Note that the components can be linearly added in any order. The linearity also extends to multiply and divide functions. This cannot be done in the time domain.

• Fourier example

0A2A1A

3

2

1

==

=

3B0B0B

3

2

1

==

=

1041

3

2

1

==

=

ωωω

( ) t)10(2sin3t)4(2cos2t)1(2costu πππ ++=

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

( ) t)1(2costu π=

( ) t)4(2cos2tu π=

( ) t)10(2sin3tu π=



• Fourier example – swap A and B values

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

0A3A2A

3

2

1

==

=

1B0B0B

3

2

1

==

= Entirely different shape

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

0A2A1A

3

2

1

==

=

3B0B0B

3

2

1

==

=

Previous shape



• Fourier Transform pair• Time to frequency

• Frequency to time

• F(ω) is typically performed using the FFT algorithms• Introduced in 1965 by Tukey and Cooley• Embedded in data acquisition software• Freely available pre-written routines

( ) ( ) dtetfF t i 2 ωπω −∞

∞−∫=

( ) ( ) ωω ωπ deFtf t i 2∫∞

∞−

=

These general equations define how we can move in either direction from one domain to the other domain. General time based data usually requires a numerical technique.



• Defining the Fourier Transform of the autocorrelation function

• S(ω) is the symbol used for the autocorrelation function in the frequency domain

• The PSD of S(ω) is

( ) ( ) ( )dttutuT1limR

2T

2T jjTu ∫−∞→−= ττ

The t in R(t, τ ) is dropped as only stationary ergodic functions are assumed.

( ) ( ) dteRS t i ∫∞

∞−

−= ωτω

( )πω

2SPSD =

The symbol S(ω) is typically used for Power Spectral Density in MSC documentation. The division by 2π is implied. Note that when 2 π = 1.0 Hz the PSD and Power Spectrum are the same.

Power Spectrum


Power Spectral Density

• PSD example

0.0000

0.0010

0.0020

0.0030

0.0040

0.0050

0.0060

0.0070

0.0080

0.0090

0.0100

1.0 10.0 100.0

(Frequency (HZ)

(acc

eler

atio

n sq

uare

d)/H

Z

Left o r Drivers s ide PSDRig ht o r Pas senger s ide PSD

0 .000 0

0 .00 10

0 .002 0

0 .003 0

0 .004 0

0 .00 50

0 .006 0

0 .00 70

0 .008 0

0 .009 0

0 .0100

0 .0 20 .0 40 .0 60 .0 8 0 .0 10 0 .0

(Frequency (HZ)

(acc

eler

atio

n sq

uare

d)/H

Z

Left o r Drivers s id e PSDRight o r Passeng er s ide PSD

The log scale magnifies detail


Power Spectral Density cont

• PSD generation • A step by step procedure

• Given this random signal:

+g

0.0

-g

Time

The mean is assumed to be zeroThe loading is assumed to be acceleration expressed in g’s

A note on g’s. This expression of acceleration is essentially unit-less. A g acceleration in the metric system is identical to a g acceleration in the English system.



• Square the signal• This results in a non-zero mean• Squaring removes negative sign

Mean square

Time

g2

( ) ( ) ( )dttgtgT1limtR

2T

2T jjTu ∫−∞→=



• It can be shown statistically that the Square Root of the Mean Square Value (RMS) is:

• Equal to the standard deviation s of a Normal distribution• One standard deviation s or the RMS value of the signal is the

value that has a 68.3% chance of occurring • “3 s” gives a probability of 99.73% chance of occurring

( )

( )

( ) ( ) ( )

( ) ( )dttgtgT1limRMS

dttgtgT1limtR

k

XRMS

k

X

2T

2T jjT

2T

2T jjTu

k

1i

2i

k

1i

2i

2

∫

∫

∑

∑

−∞→

−∞→

=

=

=

=

=

=ψ

Previous equations



• There is now a measure of the mean amplitude of the signal as it’s RMS

• How is the signal further characterized?• Apply a filter to the original signal, to eliminate all frequencies

above say, f1• Square the signal and find the Mean Square

Time

g2

Mean square value below f1


Power Spectral Density cont• Repeat the process decreasing the value of the frequency to f2, f3, f4,

f5, …• Typical increments are 1 Hz, 0.5 Hz, 0.25 Hz

Time

g2

g2

g2




Note how the mean square decreases as the frequency cutoff decreases, eliminating more and more of the frequency content



• It is now possible to plot the variation of Mean Square with fi

Frequency

g2

Mean square valueTotal Mean square value

. . . . . .f5 f4 f3 f2 f1

decreasing frequency content

• This type of plot is called the Cumulative Mean Square (CMS) plot, or if the root terms are taken then it is the CRMS plot• It shows the frequency content of the random signal• In this case, for example, the MS value jumps considerably

between f3 and f2



• Now take the gradient of the Mean Square plot

g2/Hz

. . . . . .f5 f4 f3 f2 f1Frequency Hz

• This type of plot is called the Power Spectral Density (PSD)• It shows the frequency content of the random signal, more directly than

the CMRS• Again the g2/Hz value jumps considerably between f3 and f2• The area under the curve is the RMS



• A prime contractor will typically take many random input loadings and look at the response at a key point in a structure using a set of response PSD’s

g2/Hz g2/Hz

Frequency Hz Frequency Hz

• Enveloping this set will produce a Power Spectral Density (PSD) specification (this is not the applied PSD)• The final envelope will depend on many factors• It will be a balance between safety and cost• Effect of ‘notching’ is important


Random Analysis in MSC.Nastran

• MSC.Nastran does not calculate the PSD• The user supplies the load PSD

• Provided by the vendor• NASTRAN calculates the transfer functions

• Model built by the supplier• Loads applied by the supplier

• NASTRAN performs the random calculation using the PSD data and the transfer function

• Post processing function in the RANDOM dmap module• Or in the MSC.Random option in PATRAN


Random Analysis in MSC.Nastran - cont

• Frequency response:

uj(ω) or DISP=100

( ) ( ) ( )( )( )( ) function TransferH

j point at ResponseuDLOAD SUBCASEaF

FHu

ja

j

a

ajaj

=

=

=

∗=

ω

ωω

ωωω

Fa(ω) or RLOAD1

The transfer function can be viewed as the NASTRAN mass, damping and stiffness matrices response due to applied loads

Fa(ω) or RLOAD1



• Multiple loads or SUBCASE in Frequency Response

• Matrix format of the above

( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( )( )( ) ( ) ( ) unctionsf transfer Individual........H,H,H

j intpo at sponseReuDLOADs SUBCASE Individual........F,F,F

........FHFHFHu

jcjbja

j

cba

cjcbjbajaj

=

=

=

∗+∗+∗=

ωωω

ωωωω

ωωωωωωω

( ) [ ]⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

=

......FFF

......HHHuc

b

a

jcjbjaj ω



• Recall the autocorrelation function and the associated fourier transform

• For and individual load and response

( ) ( ) ( ) ( )( ) ( )( )

( ) ( ) ( )( ) ( ) ( )( )2ajaj

ajaj

2jj

t i jj

t i j

FHS

FHu

uS

dtetutudte0RS

ωωω

ωωω

ωω

ω ωω

∗=

∗=

=

== ∫∫∞

∞−

−∞

∞−

−



• For multiple loads contributing to the same response

• In analysis practice the load PSD spectrum is supplied

( ) [ ] [ ]

conjugate ComplexH,F

......HHH

......FFF

......FFF

......HHHS

*ji

*i

*jb

*jb

*ja

*c

*b

*a

c

b

a

Tjcjbjaj

=

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

=ω

( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )ωωω

ωωω

ωωω

*b

Taab

*b

Tbbb

*a

Taaa

FFSFFSFFS

=

=

= In typical automotive NVH analysis the spectrums are derived from the road surface profiles. Thus they are in displacement units

Cross PSD



• Substitute the supplied spectrums:

• All that is required is:• Determine the transfer functions Hjk

( ) [ ]⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

......HHH

............

...SSS

...SSS

...SSS

......HHHS*jb

*jb

*ja

cccbca

bcbbba

acabaa

Tjcjbjaj ω

This is the point were users typically get lost in random analysis with MSC.Nastran. Note that if a unit load is applied then:

H=U/(Unit Load)



• Random process summary Frequency Response

10.

Frequency

FR Output

jkH1.

Frequency

FR InputNote unit load

Random ResponseScalar operation

580.

Frequency

25.8

Frequency

jjS10.

Frequency

FR Output

jkH ( )ωjS



• General comments• Remember Sii units are squared• Calculation is done on a per Hz basis

• This is one of the properties of frequency domain calculations• The calculation is performed as a post process step

• Sometimes the PSD input and PSD response criteria envelope are supplied

• Do not mix these two PSD data• Do not confuse this with shock spectrums

• Note an autospectrum generated on a 1.0 Hz basis is also the PSD• The PSD is a measure of density - division by 1.0 Hz results in same

curve• Most test software is capable of generating a PSD from measured

data• Typically automotive testing results are acceleration


Random Analysis - Units• Units – most common user question• Supplied PSD units

• Always (something)2/Hz• May not match model units• Typically displacement or acceleration based

• Velocity based is rare in automotive• Model units

• Scaling on the loading to generate the H can be done to match the supplied PSD units

• Scaling can also be done on the supplied PSD via the RANDPS• Output units

• Will be controlled by (but not limited by)• Supplied PSD• Specifications• User conversions


Random Analysis - Units - cont

• Supplied PSD• Acceleration is common in aerospace• Automotive can be displacement (road input) or acceleration

• The ‘g’ unit is common for acceleration• This is a unitless format• Not tied to any system (metric, english or any variation)• Example:

Acceleration Conversion Conversion G’s

300 in/s2 ÷ 386.4 in/ s2 .776

300 in/s2 * 2.54 cm/in ÷ 980.1 cm/ s2 .776

300 in/s2 * 25.4 mm/in ÷ 9801. cm/ s2 .776



• Road input PSD (process method depends on OEM)• Road profile is now typically measured with a laserprofilemeter• Not a true random profile however duplication of a measurement is

impossible. The random assumption is good.• Units tend to be mm2/Hz (older measurements maybe cm2/Hz)

• Aerospace and Defense typically use acceleration input• Test based accelerometer measurements

• Automotive non-road input typically use acceleration input• Test based accelerometer measurements

• Test chambers• Road course

• Examples• Frame mounts• Seat track• Steering column



• Unit examples:

Sii Disp PSD

H - Response Model – mm Load: 1.0 displacement

PSDF

(H) 2

is done on a per Hz basis

PSDF - converted

mm2

/Hz Disp – mm/Hz (mm) 2

/Hz NA

mm2

/Hz Vel - mm/s/Hz (mm/s) 2

/Hz NA

mm2

/Hz Acc – mm/s2

/Hz (mm/s2

) 2

/Hz

G’s

(mm/s2

) 2

(1/9801) 4

/Hz

or G2

/Hz

mm2

/Hz Stress – N/mm/Hz (N/mm) 2

/Hz NA



• Unit examples:

Sii Disp PSD

H - Response Model – cm Load: 0.1 displacement

PSDF

(H) 2


PSDF - converted

mm2


/Hz NA

mm2

/Hz Vel - mm/s/Hz (mm/s) 2

/Hz NA

mm2

/Hz Acc – mm/s2

/Hz (mm/s2

) 2

/Hz

G’s

(mm/s2

) 2

(1/9801) 4

/Hz

or G2

/Hz

mm2


/Hz NA



• Unit examples:

Sii Disp PSD

H - Response Model – mm Load: 10.0 displacement

PSDF

(H) 2


PSDF - converted

cm2

/Hz Disp – cm/Hz (cm) 2

/Hz NA

cm2

/Hz Vel - cm/s/Hz (cm/s) 2

/Hz NA

cm2

/Hz Acc – cm/s2

/Hz (cm/s2

) 2

/Hz

G’s

(cm/s2

) 2

(1/980.1) 4

/Hz

or G2

/Hz

cm2

/Hz Stress – N/cm/Hz (N/cm) 2

/Hz NA



• Unit examples:

Sii Accel PSD

H - Response Model - mm Load: 1 G acceleration

PSDF

(H) 2


PSDF - converted

G2


/Hz NA

G2

/Hz Vel – mm/s/Hz (mm/s) 2

/Hz NA

G2

/Hz Acc – mm/s2

(mm/s2

) 2

/Hz (mm/s

2) 2

(1/9801) 4

/Hz

or G 2

/Hz

G2


/Hz NA



• Unit examples:Sii Accel PSD

H - Response Model - mm

Load: 1 mm/s2

acceleration

PSDF

(H) 2


PSDF - converted

G2

/Hz Disp – G2

- mm/Hz (G) 2

(mm) 2

/Hz (G)

2 (mm)

2 (9801)

2 /Hz

or (mm) 2

/Hz

G2

/Hz Vel – G2

- mm/s/Hz (G) 2

(mm/s) 2

/Hz (G)

2 (mm/s)

2 (9801)

2 /Hz

or (mm/s) 2

/Hz

G2

/Hz Acc – G2

- mm/s2

(G) 2

(mm/s2

) 2

/Hz

(G) 2

(mm/s2

) 2

(9801) 2

/Hz

or (mm/s2

) 2

/Hz alternative

(G) 2

(mm/s2

) 2

(1/9801) 2

/Hz

or (G2

) 2

/Hz

G2

/Hz Stress – G2

- N/mm/Hz (G) 2

(N/mm) 2

/Hz (G)

2 (N/mm)

2 (9801)

2 /Hz

or (N/mm) 2

/Hz


Random Problem Setup in MSC.Nastran

• Executive Control Section SOL (required)

• Only performed in frequency response• Optimization SOL 200

• DFREQ and MFREQ via the ANALYSIS entry in CASE CONTROL• Also supports multiple RANDOM entries in CASE CONTROL

Structured Solution

Direct 108Modal 111


Random Problem Setup - cont

• Case Control Section• RANDOM – select the Bulk Data RANDPS and RANDT1 entries• RCROSS – Cross PSD and Cross correlation requests (V2004) on

Bulk Data RCROSS entries• DISP/VEL/ACCEL/STRESS/STRAIN/SPCFORCES/MPCFORCES/

OLOAD• PSDF• ATOC – Autocorrelation• CRMS• RALL – PSDF, ATOC, CRMS

• XY requests (original request format)• PSDF• AUTO

V2004 only supplies binary information and does not honor the RPRINT/RPUNCH options. V2005 does honor RPRINT/RPUNCH.

Note =ALL option is not recommended



• Case Control Section - cont• RANDOM and RCROSS work as a pair• Multiple RANDOM requests can be done with an alter• Any output request with PSDF, ATOC, CRMS or RALL must appear

above all subcases• PSDF, ATOC, CRMS or RALL work on all output of the grid/element

• No method to subselect a DOF or single element component at Case Control level



• Bulk Data Section• RANDPS – select the Bulk Data TABRND and supply optional

scaling factors• TABRND1 – Table of PSD values: (something)2, Hz entries• RANDT1 – Time lag τ for autocorrelation calculation

• AUTO on XY request• RCROSS

• Cross correlation and Cross PSD are calculated


BULK DATA Entries - Details

• All read by IFP and checked for errors• Stored in the datablock named DYNAMICS• Only used when referenced by a CASE CONTROL entry• Entries covered

• RANDPS• TABRND1• RCROSS


RANDPS

• J and K• SUBCASE numbers for the Hjk• K≥J

• X and Y• Scale factors for the PSD values (X for real, Y for imaginary)

• TID• TABRND1 table entry of the PSD vs frequency

RANDPS - cont

• K≥J Why?• Example: Two loads with a cross PSD spectrum

( ) ( ) ( ) ( )200,200100,100146,1452

200,200352

100,10025 HHS2HSHSS ++=ω

RANDOM = 20$SUBCASE 100LABEL = Right side inputDLOAD = 1023$SUBCASE 100LABEL = Left side inputDLOAD = 2023BEGIN BULKRANDPS, 20,100, 100, 1.0, , 25RANDPS, 20,200, 200, 1.0, , 35$RANDPS, 20,200, 100, 1.0, 0.0 , 145RANDPS, 20,200, 100, 0.0, 1.0 , 146

The assumption is Sab=Sba. Thus internally Nastran only needs Sab or Sba. As a convience for the user and efficiency it was chosen that only Sba need be defined.

Note that Sab is complex and requires the real and imaginary PSD information, thus TWO RANDPS entries.



TABRND1

• F1 – frequency g1 – PSD value (real or imaginary)• Two points minimum to define the curve

• XAXIS and YAXIS • LINEAR is the default, either or both can be LOG

• Extrapolation• Do not allow negative values for PSD to be generated

TABRND1 - cont

• Example:

TABRND1, 25, , , , , , , ,, 1.0, 1.0, 1000.0, 1.0, ENDTTABRND1, 35, , , , , , , ,, 1.0, 1.0, 1000.0, 1.0, ENDTTABRND1, 145, , , , , , , ,, 1.0, 1.0, 1000.0, 1.0, ENDTTABRND1, 146, , , , , , , ,, 1.0, 1.0, 1000.0, 1.0, ENDT

This is building up to be part of the demonstration problem. A PSD magnitude of 1.0 is assumed to allow simple hand calculation verifications.



RCROSS

• RTYPE is the H• DISP/VEL/ACCEL/STRESS/STRAIN/SPCFORCES/MPCFORCES/ OLOAD• No restriction on what can be cross computed

• ID selects element or grid component• Element components defined in QRG section 6

• Used for Cross Correlation and Cross PSDF

RCROSS - cont

• Example:

RCROSS, 888, DISP, 6, 2, DISP, 6, 2RCROSS, 888, DISP, 11, 2, DISP, 11, 2RCROSS, 888, DISP, 11, 2, DISP, 6, 2

Or

RCROSS 100 FORCE 202 167 FORCE 3302 6 1330202 RCROSS 100 STRESS 201 16 STRESS 3301 7 2330102RCROSS 100 FORCE 9902 6 STRESS 9901 7 2990106RCROSS 100 STRESS 9901 7 FORCE 9902 6 2990108RCROSS 100 SPCF 3305 3 DISP 3306 3 4641306RCROSS 100 FORCE 202 167 SPCF 3305 3 4641308

Note that there are no entries that allow entry of SUBCASE ID. This has a direct limitation on the cross correlation computations (not the cross PSD computations.)



RCROSS - cont

• Equations (V2004 Release Guide):

Cross correlation in time domain

Time and frequency domain relations

Cross PSD spectrum calculation

The Cross PSD includes all SUBCASES (j and k) identified on theRANDPS entry. The b and a values are the response quantities


CASE CONTROL Entries - Details

• All read by IFP and checked for errors• Stored in the datablock named CASECC• Entries covered (note the names are the same as BULK DATA)

• RANDOM• RCROSS


RANDOM

• Selects one set of RANDPS• Must be above all SUBCASEs• H from each SUBCASE is used according to the RANDPS

descriptions in the BULK DATA• Random calculations are a post process event in the

RANDOM module• Fluid/structure participations performed by this module


RCROSS

CORF

• Selects one set of RCROSS BULK DATA entries• Must be above all SUBCASEs• Uses the PSD responses from the RANDOM selection

• PSDF selects the cross PSD spectrum calculation• CORF selects the cross spectrum calculation• RALL selects PSDF and CORF


Random Response Output• Output request history

• V70.5 – XY output requests in plot section only method for obtaining random results

• V2001 – New options appear on the acce, disp, velocity, force, oload, spcf, mpcf, stress, and strain requests

• V2001 only binary output produced by added options• QRG did not mention this limitation• Binary datablocks intended for MSC.Fatigue

• V2004 upwards printed/punched output available


Random Response Output - cont

• PSDF – Power Spectral Density Function• Every DOF of a grid are processed• = ALL will produce very large files, binary and ASCII

• ATOC – AuTO Correlation • H2 of the function• This is not RCROSS output between two different H

• CRMS – Cumulative Root Mean Square


Random Response Output (cont.)Format for Disp (cont.):

where

PSDF—request output for auto power spectral density functionATOC—request output for auto correlation functionCRMS—request output for cumulative root mean square RALL—request output for psdf, atoc, and crmsRPRINT—request printed output in the f06 fileRPUNCH—request punch outputNORPRINT—none of the above output

• Log-Log option available when computing RMS, N0, and CRMS• Param,rmsint,log-log


HOW DO WE USE RANDOM RESULTS?

• RMS values • Area under XY curve if plotting PSD• Plot as contours for stress etc.• Factored by 3 to give 3σ probability of exceedance• RMS gives mean stress for fatigue

• PSD Plot• Shows response compared to input PSD• Important frequencies are seen

• Number of positive crossings • A statistical calculation predicts how many zero crossings will

occur per unit time of response• This is also known as apparent frequency and gives cycle count for

fatigue

• Cumulative RMS plot• Shows which frequencies contribute the most


HOW DO WE USE RANDOM RESULTS? (Cont.)

• Autocorrelation plots • Gives an indication of the degree of randomness of a

response• The signal is multiplied by itself with different phase

shifts• If a signal is non-random (sine function, square wave

etc.) then a broad correlation is seen• If a signal is highly random then the autocorrelation

output is very ‘peaky’


Random Response Analysis Example:

• The following simplified car model is subjected to random loadings that are fully correlated at the front and back wheels

• Output request:• The auto psdf disp, RMS, CRMS, N0 at grid points 1,2, and 5• The cross psdf displacement output between grid 1 (t2 ) and grid 2 (t2)


Random Response Analysis (cont.)

SOL 108 $ CENDTITLE = SIMPLE CAR WITH RANDOM INPUTSPC = 100FREQUENCY = 1000set 50 = 1,2,5disp(phase,psdf,crms) = 50rcross(phase,psdf) = 100$random = 1000SUBCASE 1DLOAD = 111

SUBCASE 2DLOAD = 112

$output (xyplot)xtitle = frequency (hz)ytitle = disp psd at grid pt 5xypunch disp psdf /5(t2)$BEGIN BULK

$$ 2 3 4 5 6 7 8 9 10RCROSS 100 DISP 1 2 DISP 2 2$FREQ1 1000 0.1 .05 40$$ DEFINE THE INPUT PSD$ 2 3 4 5 6 7 8 9 10RANDPS 1000 1 1 1. 0. 145RANDPS 1000 2 2 1. 0. 145RANDPS 1000 1 2 1. 0. 146RANDPS 1000 1 2 0. 1. 147TABRND1 145

.1 .1 5. 1. 10. .05 ENDT$..

ENDDATA

Example (cont):


Random Response Analysis (cont.)Example (cont):



EXAMPLE(cont.):


Random Analysis Recommendations

• Most spectra are given as a log function. Use the log features on the TABRND1 entry if PSD is given in log scale.

• Always generate the output PSD at the input location if possible.

• Plot the output PSD. Do not use the summary output blindly.

• Use several frequencies in the vicinity of each mode. For the modal method, a combination of FREQ1 (or FREQ2) and FREQ4 usually works best.

• For low frequencies (<20 Hz), use many frequencies since the displacement spectra is changing rapidly for a constant input acceleration.


Problem #10

Random Response With Single Input


Problem #10 - Random Response With Single Input

• For the plate model below, apply a base motion in the z-direction using the following power spectral density, (PSD).

• Connect the left edge with an RBE2 to grid point 9999 and apply the enforced motion at grid point 9999

• Use modal solution

55

33

y

x

9999Frequency (Hz) G2/Hz

20 0.130 1100 1500 0.1

1000 0.1

Autospectra of the Base Excitation


Problem #10 - Random Response With Single Input (Cont.)

• Assume a constant critical damping ratio of 3% across the whole frequency range.

• Use a log-log input for the PSD.

• Determine the acceleration PSD response at the drive point (grid point 9999) and at the corner and center of the free edge (grid points 33 and 55)

• Request output in both print and xyplot format


Solution File for Problem # 10ID SEMINAR, PROB10 SOL 111CEND TITLE= RANDOM ANALYSIS - BASE EXCITATIONSUBTITLE= USING THE MODAL METHOD WITH LANCZOSECHO= UNSORTEDSPC= 101SET 111= 33, 55, 9999ACCELERATION (rall, PHASE)= 111METHOD= 100FREQUENCY= 100SDAMPING= 100RANDOM= 100DLOAD= 100$OUTPUT(XYPLOT)XTGRID= YESYTGRID= YESXBGRID= YESYBGRID= YESYTLOG= YESXTITLE= FREQUENCYYTTITLE= ACCEL RESPONSE BASE, MAGNITUDEYBTITLE= ACCEL RESPONSE AT BASE, PHASEXYPLOT ACCEL RESPONSE / 9999 (T3RM, T3IP)YTTITLE= ACCEL RESPONSE AT TIP CENTER, MAGNITUDEYBTITLE= ACCEL RESPONSE AT TIP CENTER, PHASEXYPLOT ACCEL RESPONSE / 33 (T3RM, T3IP)YTTITLE= ACCEL RESPONSE AT OPPOSITE CORNER, MAGNITUDEYBTITLE= ACCEL RESPONSE AT OPPOSETE CORNER, PHASEXYPLOT ACCEL RESPONSE / 55 (T3RM, T3IP)$$ PLOT OUTPUT IS ONLY MEANS OF VIEWING PSD DATA$XGRID= YESYGRID= YESXLOG= YESYLOG= YESYTITLE= ACCEL P S D AT LOADED CORNERXYPLOT ACCEL PSDF / 9999(T3)YTITLE= ACCEL P S D AT TIP CENTERXYPLOT ACCEL PSDF / 33(T3)YTITLE= ACCEL P S D AT OPPOSITE CORNERXYPLOT ACCEL PSDF / 55(T3)

$

BEGIN BULKPARAM,COUPMASS,1PARAM,WTMASS,0.00259$INCLUDE 'plate.bdf'$GRID, 9999, , 0., 1., 0.$RBE2, 101, 9999, 12345, 1, 12, 23, 34, 45$SPC1, 101, 12456, 9999$$ EIGENVALUE EXTRACTION PARAMETERS$ EIGRL, 100 , , 2000.$$ SPECIFY MODAL DAMPING$TABDMP1, 100, CRIT, +, 0., .03, 10., .03, ENDT$$ POINT LOADING AT TIP CENTER$RLOAD2, 100, 600, , , 310,,Aspcd,600,9999,3,1.0spc1,101,3,9999$ TABLED1, 310, +, 10., 1., 1000., 1., ENDT$$ SPECIFY FREQUENCY STEPS$FREQ,100,30.FREQ1,100,20.,20.,50FREQ4,100,20.,1000.,.03,5$ $ SPECIFY SPECTRAL DENSITY$RANDPS, 100, 1, 1, 1., 0., 111$TABRND1, 111,LOG,LOG +, 20., 0.1, 30., 1., 100., 1., 500., .1, +, 1000., .1, ENDT$ENDDATA


Partial Output File For Problem #10POINT-ID = 33

A C C E L E R A T I O N V E C T O R( POWER SPECTRAL DENSITY FUNCTION )

FREQUENCY TYPE T1 T2 T3 R1 R2 R32.000000E+01 G 5.221806E-23 1.118822E-23 1.072273E-01 6.943391E-21 9.165858E-06 2.328869E-253.000000E+01 G 2.803730E-21 6.009700E-22 1.171296E+00 3.727297E-19 4.929606E-04 1.259152E-234.000000E+01 G 9.650047E-21 2.069631E-21 1.328467E+00 1.282579E-18 1.700663E-03 4.376034E-236.000000E+01 G 6.368169E-20 1.367993E-20 1.937050E+00 8.458521E-18 1.129787E-02 2.968235E-22

A C C E L E R A T I O N V E C T O R( ROOT MEAN SQUARE )

POINT ID. TYPE T1 T2 T3 R1 R2 R333 G 6.151087E-08 3.206081E-08 9.228085E+01 6.807472E-07 4.589051E+01 1.779829E-0855 G 6.573950E-08 2.352577E-08 9.166653E+01 1.969690E+00 4.610466E+01 1.348254E-08

9999 G 0.0 0.0 1.561982E+01 0.0 0.0 0.0

A C C E L E R A T I O N V E C T O R( NUMBER OF ZERO CROSSINGS )

POINT ID. TYPE T1 T2 T3 R1 R2 R333 G 4.218313E+02 5.318538E+02 3.924332E+02 3.697856E+02 7.319446E+02 8.260611E+0255 G 5.441308E+02 5.499335E+02 3.846914E+02 8.502590E+02 7.328255E+02 8.169711E+02

9999 G 0.0 0.0 3.991722E+02 0.0 0.0 0.0


XYPLOT Output for Problem 10X Y - O U T P U T S U M M A R Y ( R E S P O N S E )

0 SUBCASE CURVE FRAME CURVE ID./ XMIN-FRAME/ XMAX-FRAME/ YMIN-FRAME/ X FOR YMAX-FRAME/ X FORID TYPE NO. PANEL : GRID ID ALL DATA ALL DATA ALL DATA YMIN ALL DATA YMAX

0 1 ACCE 1 9999( 5,--) 2.000000E+01 1.020000E+03 9.999999E-01 1.316838E+02 1.000000E+00 1.000000E+022.000000E+01 1.020000E+03 9.999999E-01 1.316838E+02 1.000000E+00 1.000000E+02

0 1 ACCE 1 9999(--, 11) 2.000000E+01 1.020000E+03 0.000000E+00 2.000000E+01 0.000000E+00 2.000000E+012.000000E+01 1.020000E+03 0.000000E+00 2.000000E+01 0.000000E+00 2.000000E+01

0 1 ACCE 2 33( 5,--) 2.000000E+01 1.020000E+03 1.008510E+00 3.800000E+02 2.621251E+01 1.336891E+022.000000E+01 1.020000E+03 1.008510E+00 3.800000E+02 2.621251E+01 1.336891E+02

0 1 ACCE 2 33(--, 11) 2.000000E+01 1.020000E+03 1.044886E+01 1.020000E+03 3.599818E+02 2.000000E+012.000000E+01 1.020000E+03 1.044886E+01 1.020000E+03 3.599818E+02 2.000000E+01

0 1 ACCE 3 55( 5,--) 2.000000E+01 1.020000E+03 1.000853E+00 3.800000E+02 2.617639E+01 1.336891E+022.000000E+01 1.020000E+03 1.000853E+00 3.800000E+02 2.617639E+01 1.336891E+02

0 1 ACCE 3 55(--, 11) 2.000000E+01 1.020000E+03 1.055883E+01 1.020000E+03 3.599818E+02 2.000000E+01

X Y - O U T P U T S U M M A R Y ( A U T O O R P S D F )0 PLOT CURVE FRAME CURVE ID./ RMS NO. POSITIVE XMIN FOR XMAX FOR YMIN FOR X FOR YMAX FOR X FOR*TYPE TYPE NO. PANEL : GRID ID VALUE CROSSINGS ALL DATA ALL DATA ALL DATA YMIN ALL DATA YMAX

0 PSDF ACCE 4 9999( 5) 1.561982E+01 3.991722E+02 2.000E+01 1.020E+03 1.000E-01 6.689E+02 1.000E+00 1.000E+02




Output File For Problem #10 (Cont.)


Problem #11

Random Response With Multiple Inputs


Problem #11 - Random Response With Multiple Inputs

Using the modal method, determine the displacement response spectrum of the tip center point due to the input spectrum of the pressure and point loads listed below. Use the complex matrix representation (SAB) for the cross spectrum.

Frequency (Hz) psi/Hz Frequency (Hz) lb/Hz20 0.1 20 0.530 1 30 2.5100 1 500 2.5500 0.1 1000 0

1000 0.1

Autospectra of Pressure Load Auto Spectra of Corner Load

Frequency (Hz) Real Part Imaginary Part20 -0.099619 0.007816100 -0.498097 0.043579500 0.070711 -0.070711

1000 0 0

Cross-Spectrum of Pressure and Corner Loads Real/Imaginary


Problem #11 - Random Response With Multiple Inputs

Request Auto psdf and CRMS displacement output at grid points 11, 33, and 55Request cross spectrum displacement output between grid point 11direction 3 and grid point 55 direction 3


Solution File for Problem 11$$ soln11.dat$ID SEMINAR, PROB11SOL 111CEND TITLE= FREQUENCY RESPONSE WITH PRESSURE AND POINT LOADSSUBTITLE= USING THE MODAL METHOD WITH LANCZOSECHO= UNSORTEDSPC= 1SET 111= 11, 33, 55DISPLACEMENT(PLOT, PHASE)= 111ACCELERATION(PLOT,PHASE) = 111METHOD= 100FREQUENCY= 100SDAMPING= 100RANDOM= 100DISP(PSDF,CRMS,PHASE)=111RCROSS(PSDF,PHASE)=1000SUBCASE 1LABEL= PRESSURE LOADDLOAD= 100SUBCASE 2LABEL = CORNER LOADDLOAD= 200$

$OUTPUT (XYPLOT)$XTGRID= YESYTGRID= YESXBGRID= YESYBGRID= YESYTLOG= YESYBLOG= NOXTITLE= FREQUENCY (HZ)YTTITLE= DISPLACEMENT RESPONSE AT LOADED CORNER, MAGNITUDEYBTITLE= DISPLACEMENT RESPONSE AT LOADED CORNER, PHASEXYPLOT DISP RESPONSE / 11 (T3RM, T3IP)YTTITLE= DISPLACEMENT RESPONSE AT TIP CENTER, MAGNITUDEYBTITLE= DISPLACEMENT RESPONSE AT TIP CENTER, PHASEXYPLOT DISP RESPONSE / 33 (T3RM, T3IP)YTTITLE= DISPLACEMENT RESPONSE AT OPPOSITE CORNER, MAGNITUDEYBTITLE= DISPLACEMENT RESPONSE AT OPPOSITE CORNER, PHASEXYPLOT DISP RESPONSE / 55 (T3RM, T3IP)$$ PLOT OUTPUT IS ONLY MEANS OF VIEWING PSD DATA$XGRID= YESYGRID= YESXLOG= YESYLOG= YESYTITLE= DISP P S D AT LOADED CORNERXYPLOT DISP PSDF / 11(T3)YTITLE= DISP P S D AT TIP CENTERXYPLOT DISP PSDF / 33(T3)YTITLE= DISP P S D AT OPPOSITE CORNERXYPLOT DISP PSDF / 55(T3)


Solution for Problem 11 (cont.)$$ SPECIFY FREQUENCY STEPS$FREQ1, 100, 20., 20., 49$RCROSS,1000,DISP,11,3,DISP,55,3$$ SPECIFY SPECTRAL DENSITY$RANDPS, 100, 1, 1, 1., 0., 100RANDPS, 100, 2, 2, 1., 0., 200RANDPS, 100, 1, 2, 1., 0., 300RANDPS, 100, 1, 2, 0., 1., 400$TABRND1, 100, +, 20., 0.1, 30., 1., 100., 1., 500., .1,+, 1000., .1, ENDT$TABRND1, 200, +, 20., 0.5, 30., 2.5, 500., 2.5, 1000., 0.,+, ENDT$TABRND1, 300, +, 20., -.099619, 100., -.498097, 500., .070711, 1000., 0.,+, ENDT$TABRND1, 400, +, 20., .0078158, 100., .0435791, 500., -.70711, 1000., 0.,+, ENDT$ENDDATA

$BEGIN BULKPARAM,COUPMASS,1PARAM,WTMASS,0.00259$$ MODEL DESCRIBED IN NORMAL MODES EXAMPLE$INCLUDE 'plate.bdf'$$ EIGENVALUE EXTRACTION PARAMETERS$EIGRL, 100, 10., 2000.$$ SPECIFY MODAL DAMPING$TABDMP1, 100, CRIT, +, 0., .03, 10., .03, ENDT$$ FIRST LOADING$RLOAD2, 100, 400, , , 310$TABLED1, 310, +, 10., 1., 1000., 1., ENDT$$ UNIT PRESSURE LOAD TO PLATE$PLOAD2, 400, 1., 1, THRU, 40$$ SECOND LOADING$RLOAD2, 200, 600, , , 310$$ POINT LOAD AT TIP CENTER$FORCE,600,11,,1.,0.,0.,1.


Partial Output for Problem 11X Y - O U T P U T S U M M A R Y ( R E S P O N S E )0 SUBCASE CURVE FRAME CURVE ID./ XMIN-FRAME/ XMAX-FRAME/ YMIN-FRAME/ X FOR YMAX-FRAME/ X FOR

ID TYPE NO. PANEL : GRID ID ALL DATA ALL DATA ALL DATA YMIN ALL DATA YMAX0 1 DISP 1 11( 5,--) 2.000000E+01 1.000000E+03 5.214993E-04 1.000000E+03 2.645494E-01 1.400000E+02

2.000000E+01 1.000000E+03 5.214993E-04 1.000000E+03 2.645494E-01 1.400000E+020 1 DISP 1 11(--, 11) 2.000000E+01 1.000000E+03 1.937994E+01 1.000000E+03 3.594682E+02 2.000000E+01

2.000000E+01 1.000000E+03 1.937994E+01 1.000000E+03 3.594682E+02 2.000000E+010 2 DISP 2 11( 5,--) 2.000000E+01 1.000000E+03 7.341043E-05 3.800000E+02 6.694620E-02 1.400000E+02










2.000000E+01 1.000000E+03 7.973937E+00 7.599999E+02 3.594539E+02 2.000000E+01


Partial Output for Problem 11POINT-ID = 11

D I S P L A C E M E N T V E C T O R( POWER SPECTRAL DENSITY FUNCTION )

FREQUENCY TYPE T1 T2 T3 R1 R2 R32.000000E+01 G 4.512084E-26 3.431557E-26 7.947328E-05 2.155795E-07 6.016012E-06 9.237305E-274.000000E+01 G 6.754179E-25 5.141231E-25 1.189875E-03 1.059814E-06 8.969509E-05 1.384773E-256.000000E+01 G 8.361596E-25 6.367668E-25 1.465137E-03 1.070977E-06 1.104442E-04 1.718074E-258.000000E+01 G 1.228085E-24 9.360593E-25 2.142037E-03 1.086197E-06 1.618793E-04 2.531292E-25

D I S P L A C E M E N T V E C T O R( ROOT MEAN SQUARE )

POINT ID. TYPE T1 T2 T3 R1 R2 R311 G 3.290778E-11 2.880917E-11 1.376854E+00 8.629129E-02 3.851210E-01 1.505975E-1133 G 4.093889E-11 1.891101E-11 1.377021E+00 8.664111E-02 3.844410E-01 3.661771E-1255 G 3.929579E-11 1.378596E-11 1.378706E+00 8.410326E-02 3.849473E-01 3.210349E-12

1 MARCH 5, 2004 MSC.NASTRAN 9/23/03 PAGE 47

0 RANDOM 100

D I S P L A C E M E N T V E C T O R( NUMBER OF ZERO CROSSINGS )

POINT ID. TYPE T1 T2 T3 R1 R2 R311 G 1.357285E+02 1.362113E+02 1.401700E+02 6.491689E+02 1.503498E+02 1.396969E+0233 G 1.366455E+02 1.368244E+02 1.360215E+02 6.552164E+02 1.492609E+02 1.551286E+0255 G 1.369874E+02 1.370939E+02 1.432664E+02 6.581000E+02 1.498830E+02 1.406236E+02

1 MARCH 5, 2004 MSC.NASTRAN 9/23/03 PAGE 48

0 RANDOM 100 POINT-ID = 11

D I S P L A C E M E N T V E C T O R( CUMULATIVE ROOT MEAN SQUARE )

FREQUENCY TYPE T1 T2 T3 R1 R2 R32.000000E+01 G 0.0 0.0 0.0 0.0 0.0 0.04.000000E+01 G 2.684285E-12 2.341877E-12 1.126653E-01 3.571265E-03 3.093721E-02 1.215379E-126.000000E+01 G 4.724528E-12 4.122291E-12 1.981000E-01 5.836252E-03 5.439213E-02 2.140092E-128.000000E+01 G 6.554663E-12 5.720275E-12 2.744364E-01 7.458793E-03 7.537731E-02 2.971424E-121.000000E+02 G 8.933030E-12 7.798986E-12 3.734311E-01 8.809524E-03 1.027079E-01 4.054959E-121.200000E+02 G 1.479724E-11 1.293186E-11 6.180981E-01 1.001494E-02 1.708698E-01 6.735584E-12


Partial Output for Problem 11FREQUENCY RESPONSE WITH PRESSURE AND POINT LOADS MARCH 5, 2004 MSC.NASTRAN 9/23/03 PAGE 52

USING THE MODAL METHOD WITH LANCZOS 0 PRESSURE LOAD RANDOM 100

SEQUENTIAL CURVE-ID = 1C O M P L E X C R O S S - P O W E R S P E C T R A L D E N S I T Y F U N C T I O N

(MAGNITUDE/PHASE)0 RCROSS RTYPE1 ID1 COMP1 RTYPE2 ID2 COMP2 CURID0 1000 DISP 11 3 DISP 55 3 0

FREQUENCY CPSDF FREQUENCY CPSDF2.000000E+01 7.782711E-05 / 359.7912 4.000000E+01 1.169207E-03 / 359.98176.000000E+01 1.446440E-03 / 359.9715 8.000000E+01 2.125043E-03 / 359.96511.000000E+02 4.256193E-03 / 359.9659 1.200000E+02 1.995366E-02 / 0.02061.400000E+02 5.931298E-02 / 0.0270 1.600000E+02 3.981690E-03 / 359.96411.800000E+02 1.110766E-03 / 359.8067 2.000000E+02 4.651507E-04 / 359.52292.200000E+02 2.361837E-04 / 359.0721 2.400000E+02 1.342108E-04 / 358.40122.600000E+02 8.205518E-05 / 357.4377 2.800000E+02 5.276162E-05 / 356.08123.000000E+02 3.515652E-05 / 354.1868 3.200000E+02 2.402328E-05 / 351.53853.400000E+02 1.670592E-05 / 347.8049 3.600000E+02 1.176429E-05 / 342.46553.800000E+02 8.387206E-06 / 334.7123 4.000000E+02 6.119115E-06 / 323.42144.200000E+02 4.722277E-06 / 307.6403 4.400000E+02 4.072001E-06 / 288.29084.600000E+02 4.034619E-06 / 269.2190 4.800000E+02 4.427421E-06 / 253.87995.000000E+02 5.106795E-06 / 242.7013 5.200000E+02 5.390142E-06 / 236.15725.400000E+02 5.879031E-06 / 229.9111 5.600000E+02 6.667262E-06 / 223.85395.800000E+02 7.941909E-06 / 217.8872 6.000000E+02 1.009843E-05 / 211.92926.200000E+02 1.407104E-05 / 205.9172 6.400000E+02 2.244281E-05 / 199.81126.600000E+02 4.367881E-05 / 193.5947 6.799999E+02 9.592201E-05 / 187.27146.999999E+02 7.964316E-05 / 180.8491 7.200000E+02 2.743966E-05 / 174.29297.400000E+02 1.057218E-05 / 167.3723 7.599999E+02 4.433171E-06 / 158.94037.800000E+02 1.351510E-06 / 138.3461 8.000000E+02 1.558493E-06 / 1.16148.200000E+02 5.536478E-06 / 343.4609 8.399999E+02 1.063914E-05 / 337.73128.600000E+02 6.950111E-06 / 334.6017 8.800000E+02 2.748527E-06 / 332.94028.999999E+02 1.156801E-06 / 332.4832 9.199999E+02 5.375278E-07 / 333.20769.400000E+02 2.648299E-07 / 335.2508 9.600000E+02 1.325349E-07 / 339.02119.799999E+02 6.395399E-08 / 345.7172 1.000000E+03 2.718711E-08 / 359.9906


Partial Output for Problem 11

X Y - O U T P U T S U M M A R Y ( A U T O O R P S D F )0 PLOT CURVE FRAME CURVE ID./ RMS NO. POSITIVE XMIN FOR XMAX FOR YMIN FOR X FOR YMAX FOR X FOR*TYPE TYPE NO. PANEL : GRID ID VALUE CROSSINGS ALL DATA ALL DATA ALL DATA YMIN ALL DATA YMAX

0 PSDF DISP 7 11( 5) 1.376854E+00 1.401700E+02 2.000E+01 1.000E+03 2.720E-08 1.000E+03 5.926E-02 1.400E+02




Partial Output For Problem #11 (Cont.)


So what is MSC.Random?• User-developed MSC.Patran application

• Customer-requested features and functions• Officially available since MSC.Patran v9

• Available under Utilities/Analysis menu• Improved setup for Frequency Response Analysis• .xdb access of Frequency Response results• Enhanced Random Analysis calculations done “on the

fly”• RMS fringe plots• Specialized XY-Plotting• Interactive v. batch environment


MSC.Random Benefits• Simplified analysis setup

• GUI interface• Engineer-driven specialized forms• No XYPLOT entries required• Full on-line help

• Improved productivity• .xdb access of results• Re-analyze without restarting

• Quality results• Specialized interactive plots• Log-log integration• Cumulative RMS


Random Analysis: The OLD Way• Make model• Set up Frequency Response unit case

• RLOAD, DAREA, TABLED1, CONM2, SUPORT, FREQi, TABDMP1, WTMASS

• Set up RANDOM entries• RANDPS, TABRND1, XYPLOT

• Run Frequency Response + Random in MSC.Nastran• View batch XYPlots and .f06 files for results


Random Analysis: The NEW Way• Make Model• Select base-drive point and which way(s)

you will shake it• Unit loading(s) bulk data and Case Control

cards automatically generated• Run (just) the Frequency Response

analysis in MSC.Nastran• Define PSDF spectrum tables in

MSC.Patran• Run Random inside MSC.Patran• Interactive XYPlots• RMS Fringe Plots


MSC.Random - Driven by ONE (1) Form

This button brings up the Advanced Frequency Output sub-form. See next page for details

Chose the type of Random input. Choices are Base Input, Forced Input and Acoustic.

The Job Name defaults to the database name. It will be used to name result file and .log file names.

Select the base input node and the directions for the input. One loadcase will be created for each direction.

Select the damping field. This has to be created in MSC.Patran prior to entering this form. The damping fields are created using Field Application. The fields must be created as Non-Special and Frequency Dependent.

This will open a sub-form for selecting the desired output. See the next page for details.

Input the frequency range of interest. This will be used for the FREQi and EIGRL cards. The EIGRL start frequency is hardwired to -.01 to capture the rigid body modes. If this is not done, nodal responses will be relative to the input node.

The Input and WtMass are used to set the DAREA value and for converting to Gs when doing acceleration XY Plots. It is critical that this information is correct. See Units discussion form details on these parameters.

Choices : Freq. Response, RMS Analysis, Read RMS, XYplot


MSC.Random - Results• Interactive XY Plotting:

PSDF Plots• Interactive picking of

nodes/elements• Acceleration scale

defaults to g’s• RMS and No. of zero

crossings reported• Option to specify

frequency range for RMS

• Total and interval RMS values reported


Interactive XY Plotting: PSDF Plots• Interactive picking

of nodes/elements• Acceleration scale

defaults to g’s• RMS and No. of

zero crossings reported

• Option to specify frequency range for RMS• Total and

interval RMS values reported


Interactive XY Plotting: PSDF PlotsEasy to apply new input PSDF Spectrum


Interactive XY Plotting: PSDF PlotsIncludes correctly calculated VonMises Stresses


Cumulative RMS Plots


Autocorrelation Plots


MSC.Random - RMS Fringe Plots• Interactive fringe

plots of RMS values

• Use with primaryoutput quantities (i.e. Sx, Sy, Sxy)

• Derived quantities (Principals or VonMises) will be calculated on primary RMS values


MSC.Random in MSC.Patran• Interactive RANDOM analysis from within the MSC.Patran

environment• Eliminates need for XYPLOT cards for each output

quantity and item code• Fast access of results from .xdb database• Rapid re-analysis for new input PSDs without

re-running MSC.Nastran• Enhanced XY plots for PSDF, CRMS, Auto• Exclusive RMS fringe plots


Purpose of MSC.RandomWhat is MSC.Random?

• MSC.Random is a program that calculates random responses based on the results of a MSC.Nastran Frequency Response Analysis (.xdb format - Param,Post,0)

• MSC.Random is compatible with MSC.Nastran (V68.2, V69, V70, V70.5) and MSC.Patran V7.5 and higher.

How can MSC.Random help me?

• Faster analysis turn-around time.• Simplified analysis using graphical interface.• Eliminates the need to create XYPEAK/XYPLOT cards.• Facilitates results post-processing.


MSC.Random - FlowchartMSC.Patran

MSC.Random

MSC.NastranFrequency Response Analysis (.xdb)

Freq. Response Input

MSC.PatranRandom Input

MSC.Patran

XY Plot (PSDF, Auto Corr., Crms) RMS Contour (Accel, Disp, Stress, Force etc).


MSC.Random AdvantagesMSC.Random can be executed within MSC.Patran via the MSC.Random menu system

Random analysis performed using results from a harmonic analysis with unit load input, therefore MSC.Nastran does not have to be re-run for given changes to the random input spectrum.

RMS results can be plotted on the entire model using MSC.Patran (Fringe Plots)

XY- plots are easily created via a graphical selection of nodes or elements within MSC.Patran.


MSC.Random Advantages -Continued

Familiar output request such asstress = all or set numberdisplacement = allforce = all (etc…)

Supported elements: All linear elements2-D Elements: cbar, cbeam, conrod, crod, ctube, cdampi, cbush, celas1, celas2, celas3, celas4Plate Elements : cquad4, cquad8, cquadr, ctria3, ctria6, ctriar, cshearSolid Elements : chexa, cpenta, ctetraMPC’s

All response quantities in a single run:StressesForcesStrainsAccelerationsDisplacementsVelocities


MSC.Random Advantages -Continued

Complete output• Separate ASCII output for RMS response.• Complete XY plotting for Acceleration, Velocity, Displacement, Stresses; Forces; SPCF

and MPCF including PSDF and cumulative RMS response plots.• Number of positive crossings (zero crossings) computed for all output quantities.

Plotting• Fringe plots available for all response quantities through MSC.Patran.• XY plots available through MSC.Patran (PSDF, CRMS, Auto Correlation).• XY Plot option to calculate and display rms results by frequency range.• XY Plots of Von Mises stresses for plate elements.

Maintained by MSC.• Available with MSC.Nastran and MSC.Patran upgrades.


MSC.Random - Approach

Step 1:

.xdb(post,0)

Harmonic Analysis(MSC.Nastran)

Step 3:

Step 2: Random Analysis(MSC.Random)

XY Plots RMS Plots

RandomInput File

.pat file (Binary)

RMS Analysis


MSC.Random - PATRAN Interface

This button brings up the Advanced Frequency Output sub-form. See next page for details

Chose the type of Random input. Choices are Base Input, Forced Input and Acoustic.

The Job Name defaults to the database name. It will be used to name result file and .log file names.

Select the base input node and the directions for the input. One loadcase will be created for each direction.

Select the damping field. This has to be created in MSC.Patran prior to entering this form. The damping fields are created using Field Application. The fields must be created as Non-Special and Frequency Dependent.

This will open a sub-form for selecting the desired output. See the next page for details.

Input the frequency range of interest. This will be used for the FREQi and EIGRL cards. The EIGRL start frequency is hardwired to -.01 to capture the rigid body modes. If this is not done, nodal responses will be relative to the input node.

The Input and WtMass are used to set the DAREA value and for converting to Gs when doing acceleration XY Plots. It is critical that this information is correct. See Units discussion form details on these parameters.

Choices : Freq. Response, RMS Analysis, Read RMS, XYplot


Step 1: Harmonic AnalysisFor base excitation problems, use the MSC.RANDOM user interface within MSC.Patran.

• Select desired subcases by toggling the X,Y,Z directions.• Select the base input node.• Select the Damping field (Created using Fields Application).• Select output requests from the Output Requests Form.• Set the frequency range for output by setting the frequency data

From/To data boxes.• Specify the base input acceleration by entering a value for “Input”

(typically in/s2) and “Wtmass” (Parameter Wtmass).• Select Apply to create job, then select the job within Analysis

form. Select Apply to create MSC.Nastran bulk data file.

Execute MSC.Nastran to calculate harmonic response (Sol 111).

• Refer to Appendix for sample input and examples for base excitation & acoustic loading.


Step 2 - RMS (Random) Analysis

Note : Step 2 is required only if RMS contour plots are required

1

2

4

3 Click if you want to import RMS results automatically


Step 2 - RMS (Random) Analysis - Random Input

Methods:Single CaseCombine CasesExisting RANDPS file

Select existing Patran field. Used to create the TABDMP1 table.

Fill out these fields similar to the MSC.Nastran RANDPS card. The Auto Spectral Density and Uncouples toggles control the valid entries.

When this field has focus, the list box to the left will show all of the subcases in the selected XDB file.


Step 3 : XYPLOT plots

1

2

3

4

5

6

7

nodecelascbar..cquad/ctricshearsolid

dispveloaccelSPCFMPCF------ForceStressStrain

PSDFCRMS

AUTO Cor

Plot Base Node


Step 3: XYPLOT; XY PSDF


STEP 3: XYPLOT; XY CRMS


STEP 3: XYPLOT; PSDF


Step 3: RMS Contour Plots

1

2

4

Click if you want to import RMS results automatically

Freq. ResponseRMS AnalysisRead RMSXYplot

Use Read RMS optionOR

Note: Once RMS results are read in, use RESULTS menu from MSC.Patran to plot contour plots. DO NOT PLOT any derived quantity such as Von-Mises, Principal Stress. DO NOT USE ‘QUICK PLOT’, use ‘CREATE FRINGE’ option.


Step 3: Output; RMS Fringe

Harmonic Analysis Flowchart

.xdb file Subcase 1: 1G-XdirectionSubcase 2: 1G-YdirectionSubcase 3: 1G-Zdirection

MSC.Nastran Harmonic Analysis

Generate FEM

Input Loads and Damping;Subcase 1: 1G-X directionSubcase 2: 1G-Y directionSubcase 3: 1G-Z direction

Review Results;Is modal damping input acceptable?

Is model yielding meaningful results?

No

Yes

Loop 1

Transfer .xdb file to Random Analysis Flowchart, next page

Return from Random AnalysisFlowchart, previous page

Update FEM?

MSC.Patran UI Yes

No

Start


MSC.Random - Flowchart

Execute MSC.Random,Specify unique JOBNAME to differentiate load cases.

Required input; .xdb file and Random Input File

Post-Processing;Generate XY Plots, RMS Plots and

create Hardcopy Plots

.pat MSC.Patran result file

.rms ASCII result file

Generate Random Input FileGenerated for a single Subcase (Loadcase)

Loop 2

Random Analysis Data Flow

.xdb file from Harmonic Analysis Flowchart, previous page

Return to Harmonic AnalysisFlowchart, previous page

Yes

No

MSC.Patran UIMSC.Patran UI

MSC.Patran UI

Write Report End of Job

Run another load case?Modify FEM, damping

or Input Spectrum?

Yes Update Damping Table

or FEM?

No



Relative Displacement MPC PCLTo calculate the relative response between two nodes, an MSC.Nastran MPC element is used.

The “Relative Displacement MPC” PCLfacilitates in the creation of this type of MPC.

• Select the DOF for response calculation. • Select the two independent nodes.• Apply.

A dependent node (located between the two selected independent nodes) and an MPC will be created. Following the analysis; the dependent node can be selected in results post-processing to obtain the relative response between the two selected independent nodes.


SummaryMSC.Random delivers:

Base excitation analysis and limited acoustic and forced input set-up within MSC.Patran.

Random analysis submittal within MSC.Patran.

Cumulative RMS XY Plot capability.

RMS calculation within user defined frequency range.

MSC.Random on-line documentation within MSC.Patran.

MSC.Random> Better…

> Faster…> Randomly Exciting


MSC.Random Appendix:Contents:

Harmonic Analysis: Base Excitation;• Case Control • Bulk Data Example

Harmonic Analysis: Forced Excitation;• Case Control• Bulk Data Example


Step 1 : MSC.Nastran Data Deck SetupBase Excitation

ID MSC,MohanSol 111CendTitle : Base ExcitationAccel(Sort2, Real, Plot) = allStress(Sort2, Real, Plot) = allSpc = 77sdamp = 102freq = 604method = 219Subcase 101

Subtitle = X direction Unit G InputDload = 111

Subcase 102Subtitle = Y direction Unit G InputDload = 222

Begin Bulk


Step 1 : MSC.Nastran Data Deck SetupBase Excitation(cont):

Param,Wtmass,.002589param,post,0Eigrl,219,-.1,2000.Suport,99,123spc1,77,456,99conm2,999,99,,1.e8darea,11105,99,1,1.e8darea,22205,99,2,1.e8tabdmp1,102,crit+,0.0,.02,2000.,.02,endtrload1,111,11105,,,88rload1,222,22205,,,88tabled1,88+,0.0,1.0,2000.,1.0,endt$ Include other bulk data cards……..enddata


Step 1 : MSC.Nastran Data Deck SetupTypical Setup - Forced Excitation

Case Control SectionLoadset = 107 $ Always above all subcases.Spc = …

Subcase 11Dload = 100

Bulk Data Section

Rload1, 100, 302, , , 200

Lseq, 107, 302, 111

Pload4, 111, 77, 1.0, 1.0, 1.0, 1.0, thru, 123

Tabled1, 200, …


Step 1 : MSC.Nastran Data Deck Setup

Forced Excitation (e.g., Acoustic)Sol 111CendTitle : Acoustic ExcitationAccel(Real, Plot) = allStress(Real, Plot) = alletc….Spc = 202sdamp = 102freq = 99method = 50$ Loadset ID same as Lseq ID in bulk data section.Loadset = 107Subcase 117

Subtitle = Unit PSI Harmonic LoadingDload = 100

Begin Bulk


Step 1 : MSC.Nastran Data Deck Setup

Param,Wtmass,.002589Param,post,0Eigrl,50,-.1,1000.$ Rload 100 is selected by Dload in case control section. $ Darea 302 on Lseq & RloadRload1,100,302, , ,200$ Lseq 107 selected by Loadset in case control section. 111 is the static load.Lseq,107,302,111Pload4,111,369,1.0,1.0,1.0,1.0,thru,988$ Table Id 200 selected by Rload - defined input amplitude Vs. Frequency.tabled1,200+,0.0,1.0,2000.,1.0,endtspc1,202,……….tabdmp1,102,crit+,0.0,.02,2000.,.02,endt$ Include other bulk data cards……..enddata


CASE STUDY

• RANDOM VIBRATION ANALYSIS OF A SATELLITE• The purpose of this case study is to show the use of

MSC.Random in performing a Random Vibration analysis. • A satellite structure is assumed excited by the launcher

vehicle as a random acceleration loading. Both vertical and lateral cases are considered.

• We want to know the response at a station on the satellite where we intend to mount a PCB.

• First perform a Modal Frequency Response analysis using the methods shown in Section 11.

• Then execute a Random analysis in MSC.Random using the results from the Frequency Response analysis and a supplied input PSD.

• Post process the results at the station of interest using MSC.Random.


CASE STUDY• Case Study steps

1. Import a Nastran Input File that contains the representation of the satellite model.

2. Create a Frequency Dependent field of magnitude 1.0 over a frequency range of 1.0 Hz to 1000.0 Hz.

3. Create two load cases called vertical acceleration and lateral acceleration.

4. Apply the field created in Step 2 to the bottom of the satelliteto create a unit acceleration load in each direction.

5. Submit the model to MSC.Nastran for analysis.6. Create the Frequency Dependent field that contains the PSD

Input information.7. Open MSC.Random.8. Select the XDB Result Files from the Frequency Response

analysis and perform Random Vibration analysis using MSC.Random

9. Post Process results – Use MSC.Random to create Acceleration versus Frequency plots at various location.


The model is imported as usual.Create a non spatial field for frequencyresponse.Enter frequency response for the Field Name.Select Frequency as the Active IndependentVariable.Click on Input Data button.Enter the values shown in the table.

CASE STUDY


Create a load case for the verticalacceleration load:

Enter ‘vertical acceleration’ for theLoad Case Name.

Change Load Case Type to Time Dependent.

Click on Assign/Prioritize Loads/BCsbutton.

Select Displ_spc1.3 from the Select Individual Loads/BCs.

CASE STUDY


CASE STUDY

Create another load case for thelateral acceleration load:

Enter ‘lateral acceleration’ for theLoad Case Name.Make it Time Dependent

Select Displ_spc1.1 from theSelect Individual Loads/BCs.


CASE STUDY

Create the lateral acceleration load:

Make ‘lateral acceleration’ the Current Load Case

Enter lateral acceleration for theNew Set Name.Enter <1,0,0> for Translations andselect frequency_response forTime/Freq. Dependence field.

Select the nodes along the bottomedge of the exhaust cone.


CASE STUDY

Create the vertical acceleration load:

Make ‘vertical acceleration’ the Current Load case

Enter ‘vertical acceleration’ for the New Set Name.

Enter <0,0,1> for Translations and select frequency_response for Time/Freq. Dependence field.

Select the nodes along the bottomedge of the exhaust cone.


CASE STUDY

Submit the vertical acceleration load casefor frequency response analysis:

Enter satellite_vertical_acc for the job name.Select FREQUENCY RESPONSE andModal Formulation.Change the Wt-Mass Conversion to 0.00259.Change the Number of Desired Roots to 20.


CASE STUDY

Set up Subcases:

Select vertical acceleration.

Click on Subcase Parameters…

Click on DEFINE FREQUENCIES.Enter the values shown in the table.


CASE STUDY

ab

c

Select Crit. Damp. (CRIT) for Modal Damping.

Click on DEFINE MODAL DAMPING.

Enter the values shown in the table.


CASE STUDY

Click on Output Requests.Select Acceleration from theSelect Result Type box.


CASE STUDY

Click on Subcase Select.

Select vertical accelerationfrom the top box

Unselect Default from the Subcase Selected box.

Run the analysis


CASE STUDY

The results of the vertical accelerationare shown for the grid of interest 3326

The plot has been enhanced using XYPlot


CASE STUDY

GRID 3326The results for the vertical acceleration frequency response case are shown at 22.2Hz.

The dominant motion is a vertical motion of the satellite, with most of the deflection taking place in the base support ring.

The ring acts rather like a vibration isolator and filters out the vertical input.

The vertical case is discounted now and no random analysis is done on this input.


CASE STUDY

Submit the horizontal acceleration load case

for frequency response analysis:

Click on the satellite_vertical_acc in the Available Jobs box. This will allow Patran to use same setting for the Solution Type as those used in the satellite_vertical_acc analysis.Change the Job Name to satellite_lateral_acc.Repeat the same procedures as before, but choose the lateral acceleration subcases for this analysis job.Click on Subcase Select.Select lateral acceleration from Subcases For Solution Sequence box and unselect Default from the Subcases Selected box.


CASE STUDY

The results of the lateral accelerationare shown for the grid of interest 3326

The plot has been enhanced using XYPlot


CASE STUDY

GRID 3326

The results for the lateral acceleration frequency response case are shown at 22.2Hz.

The dominant motion is a bending motion of the satellite, with large deflection in the base support ring.


CASE STUDY

Create a non spatial field for the

MSC.Random analysis.Enter psd for the Field Name.Select Frequency as the Active Independent Variable.Click on Input Data button.Enter the values shown in the table.Use Fields/show to check the data.


CASE STUDY

PSD(g^2/Hz)

Freq. (Hz)

Input PSDCare must be taken with the input PSD format:

It is usually assumed that the definition is on a LOG-LOG scale.

This assumption must be checked.

Plotting the field in XYplot requires both axes scales set to LOG.

The nastran PSD definition must be set to LOG input.

Note carefully whether input is ‘g’ or acceleration units.


CASE STUDY

PSD(g^2/Hz)

Freq. (Hz)

Input PSD

To get an optimum plot for checking the PSD input:

Set y axis to a LOG scale.

Use semi-Auto method.

Pick lowest number, in this case .010.This is -2 *log10(the BASE power)select number of cycles (in this case .010 to .1 and .1 to 1is two cycles)

Do the same on the x axis.

Pick tick marks and Grid lines as required.


CASE STUDY

Open MSC.RandomUtilities / Applications / MSC.Random.Click OK when the DISCLAIMER message appears on the screen.Change the Action from Freq. Response to RMS Analysis.


CASE STUDY• Note: The Random Analysis

(RMS Analysis) is carried out on the assumption there is already FR data• Select “Freq. Response” if no

prior analysis has been carried out

• If no FR analysis has been done, select Loading type:• Base acceleration w/ large mass• Applied force(s)• Acoustic pressures


CASE STUDY• If Base Input is used

• Enforced acceleration assumed at a connected base point using large mass method

• Directions selected• Large Mass

• ID Node where large mass (1E8) will be place placed


CASE STUDY• For Force Input or

Acoustic input• Select pre-defined load case


CASE STUDY

Setup the model for Random analysis:Choose RMS analysisClick on Select XDB File.Select satellite_lateral_acc.xdb(the results from the previous Frequency Response analysis)

Select Random Input.Change the Random Input Method to Single Case.Click on the Excited Setfield and select 1:LATERAL ACCELERATION from the Available Subcases box.Click on the Input Field and select psd from the PSD Input fields box.


CASE STUDY

Select the Random Input Method to Single Case.Clicking on the Excited Set field will bring up a list of Available Subcases.The frequency response analysis should be in here.Clicking on the Input Field will give a list of all fields, and the PSD definition field should be in here.The complex X input is the scale factor.Select Auto Spectral DensitySet axes as appropriate, in this case the input is LOG - LOG


CASE STUDY

Other Options:Select the Random Input Method to Existing RANDPS FileThis will allow the user to select a .inp file, defined in MSC.Random as a Nastran .bdf fragment with RANDPS data defined


CASE STUDYa

b

Create XY Plots of the PSD Response:

Change Action to XY Plots.

Select Node 3326, which is where the PCB board will be located.

Change the Res. Type to Accel.

Set the Plot Scale to 1.0

Change Component to DOF 1.

Change the Plot Type to PSDF.


CASE STUDYNote:All labels gridlines and scales set automatically.

RMS is 5.774gSo the ‘safe’ g limit at 3*RMS is 17.32g

Apparent Frequency is 22.9 Hz, showing that Mode 1 dominates


CASE STUDYOverlay the base input and see the effect of the input PSD.

From the previous work on modal analysis and effective mass of this structure, it is assumed 50 Hz is a valid cutoff – for the first 10 modes

Base Input also plotted and full PSD

Base Input Full PSD

Analysis only up to 50 Hz


CASE STUDY

Another possibility is to go into Results and create an RMS fringe plot.

The Result Case is loaded in by the XDB attachment.

The resulting RMS plot is an RMS accn magnitude plot.

The graphical result of 5.774 g RMS agrees.


CASE STUDY

From the RMS fringe plot, it is visible that the panel local mode plays an important part in the RMS response. If there is a component located there, it will see the highest loading environment of 7.71 g RMS.To investigate further it is possible to do a PSD plot of this position (grid 3606) and see that the local mode do indeed play a major role with the first bending mode.Out of interest a grid on the support skirt is investigated and you can see it has a low RMS value and the bending mode dominates.


CASE STUDY

Based on this analysis, it is possible to provide a subcontractor with a PSD specification which is derived by enveloping the PSD response that was obtained.In the workshops which follow, the input PSD for the Printed Circuit Board is based on this type of analysis.The question could arise however about the effect of the original PSD input over the range greater than 50 Hz – could it have been significant? This is left to the student to investigate.Also note that an input PSD with a bias to the lower frequencies would be a far more damaging environment in our case.


RANDOM ANALYSIS RECOMMENDATIONS

• Most spectra are given as a log function. Use the log features on the TABRND1 entry if PSD is given in log scale.

• Always generate the output PSD at the input location if possible.

• Plot the output PSD. Do not use the summary output blindly.

• Use several frequencies in the vicinity of each mode. For the modal method, a combination of FREQ1 (or FREQ2) and FREQ4 usually works best.

• For low frequencies (<20 Hz), use many response frequencies since the displacement spectra is changing rapidly for a constant input acceleration.


WORKSHOP 9 - RANDOM ANALYSIS USING MSC.RANDOM

• Please carry out Workshop 9

• This workshop uses MSC.Random to calculate the response of a simple plate structure

• Please do not hesitate to ask your tutor’s advice.


WORKSHOP 11 - RANDOM VIBRATION ANALYSIS ON A

SATELLITE USING MSC.RANDOM

• Please carry out Workshop 11• This workshop uses

MSC.Random to calculate the response of the satellite structure as shown in the case study.

• Please do not hesitate to ask your tutor’s advice.

msc nastran random dynamics

Documents

higher order

autocorrelation

data points

statistic

t1

t1and ru

4 sig na

physical responses