Basics of Modal Testing and Analysis TN-DSA-003

Introduction

Modal analysis is a powerful tool for understanding the vibration

characteristics of mechanical structures. It simplifies the vibration response

of a complex structure by reducing the data to a set of modal parameters

that can be analyzed with relative ease. This application note discusses

the concept of modal analysis, applications where modal analysis is useful,

and techniques for the acquisition and visualization of modal data.

The Modal Domain

The modal domain is one of several different domains that help us to

understand structural vibrations. Structures vibrate in particular shapes

called mode shapes when excited at or near their resonant frequencies.

Under normal operating conditions, a structure will vibrate in a

complex combination of all its mode shapes. By analyzing the

mode shapes, it is possible to gain an understanding of the types of

vibration that the structure can exhibit. Modal analysis also reduces a

complex structure, which is not easily analyzed, into a set of single-

degree-of-freedom systems that can easily be understood.

Experimental Modal Analysis determines the mode shapes and

resonant frequencies of a structure.

For example, if you vibrate a beam at the first resonant frequency, the beam

will assume the first mode shape, often called the V mode as shown in

Figure 1. The beam will move back and forth from the position shown in

solid lines to the position shown in dashed lines. If you vibrate the beam

at the second resonant frequency, you will excite the second mode shape,

often called the S mode. If you vibrate the beam at a frequency between

the two, the deformation shape will be some combination of the two mode

shapes. The third mode shape is often called the W mode.

Figure 1. Mode shapes of a simply supported beam

Engineers use modal analysis to predict the theoretical vibration of

a structure from a finite element model. The first step is to

represent the structure as a theoretical collection of springs and

masses; then you develop a set of matrix equations that describes

the whole structure. Next, you apply a mathematical algorithm to

the matrices to extract the mode shapes and resonant frequencies

of the structure. All this theoretical work produces very practical

benefits because it allows the prediction of the modal response of

a structure. By finding and addressing potential problems early in

the design process, manufacturers save money and improve

product quality.

Once the structure is built, experimental modal analysis can

determine its actual modal response. Experimental modal analysis

consists of exciting the structure and measuring its frequency

response function (FRF) at various points.

For example, the tuning fork shown in Figure 2 is a very simple

structure. By recording its FRFs at various points, the results shown

in Figure 2 are obtained. The resonant frequencies are the peaks

that appear at the same frequency at every point on the structure.

The amplitude of the peak at each location describes the mode

shape for the associated resonant frequency. The damping of each

mode determines the sharpness of each peak. The results indicate

that for the first mode, the base is fixed and the end has maximum

displacement as shown in Figure 3. The second mode has maximum

deflection at the middle of the fork as shown in Figure 3.

Figure 2. Modal analysis of a tuning fork results in FRFs for each pointon the structure; the amplitudes at each resonant frequencydescribing the mode shape.

j u l y 2 0 0 5

2

Figure 3. The first mode shape of the tuning fork has the base fixedand the maximum deflection at the end; the second mode shape hasthe ends fixed and maximum deflection at the middle.

Modal Analysis Applications

Mode shapes and resonant frequencies of a structure (its modal response)

can be predicted by using a mathematical model known as a Finite Element

Model (FEM). An FEM uses points connected by elements possessing the

mathematical properties of the structure’s materials. Boundary conditions

define how the structure is fixed to the ground and what force loads are

applied. After defining the model, a mathematical algorithm computes the

mode shapes and resonant frequencies.

The practical benefit is that it is possible to predict the vibration response

of a structure before it is even built. Figure 4 shows a FEM of a pressurized

fuel storage tank for a space vehicle with force loads and boundary

conditions applied.

Figure 4. Finite Element Model of a space vehicle with force loads andboundary conditions.

After building the structure, it’s good practice to verify the FEM using

experimental modal analysis. This identifies errors in the model and leads

to improvements in future designs. Professionals can also use

experimental modal analysis without FEM models. In this case, the goal is

to identify the modal response of an existing structure in order to resolve

vibration problems.

One of the common vibration problems identified by modal analysis is

when a forcing function excites the resonant frequency of a structure. A

forcing function is the mechanism that forces the structure to vibrate. Real

world examples include rotating imbalance in an automobile engine,

reciprocating motion in a machine, or broadband noise from wind or road

conditions in a vehicle. The frequency of the forcing function is extracted

from a frequency domain analysis of its signal. When a resonant frequency

of the structure coincides with the frequency of the forcing function, the

structure may exhibit large vibrations that lead to fatigue and failure.

In this case, the mode-shape information can be used to redesign

or modify the structure to move the resonant frequencies away

from the forcing function. Structural elements can be added to

increase the structure’s stiffness or simple changes made to

increase or decrease the mass. These changes will act to change

the structure’s resonance frequency values.

Other techniques of vibration suppression include increasing the

damping of the structure by changing the material or by coating the

surface with viscoelastic material. Also, vibration absorbers tuned

to the forcing function frequency can be added. When other

techniques fail, active vibration controls provide a remedy. This

approach involves measuring the structural vibrations and using a

computer-driven actuator to counteract them.

Figure 5. Vibration isolators (left) and absorbers (right) are methodsof passive vibration suppression.

Figure 6. Damping treatment is the most common and activesuppression is the most expensive technique for vibration.

3

All these techniques depend on modal analysis to identify the resonant

frequencies, damping and mode shapes of the structure. Once these

characteristics are known, it is possible to isolate vibration problems

and implement effective solutions

Modal Data Acquisition

The first step in experimental modal analysis is to measure the vibration

response of the structure. This involves exciting the structure and

measuring the resulting vibrations to acquire a data set that can be used to

compute the mode shapes and resonant frequencies. Modal analysis

software interprets this data to display the mode shapes.

To excite a structure and cause it to vibrate, two common tools are used:

an impact hammer or a vibrator. An impact hammer (Figure 7) is a

specialized measurement tool that produces short duration excitation by

striking the structure at some point as shown in Figure 8.

The hammer incorporates a sensor (called a load cell) that produces a

signal proportional to the force of impact. This sensor enables precise

measurement of the excitation force exerted on the test structure. Impact

hammers are used for experimental modal analysis of structures where the

use of a mechanical vibrator is not convenient; these applications include

tests conducted in the field or on very large structures.

Different impact tips are used to tune the frequency content of the impact

force energy. For low frequency measurements, a soft rubber tip is used. A

hard metal tip is the best choice for high frequency measurements.

Figure 7. Impact hammer instrumented with a load cell to measurethe excitation force and different hardness tips.

Figure 8. Impact hammer force versus time (input1) and structuralresponse versus time (input2).

For laboratory vibration measurements, shakers are the instrument of

choice. Shakers are rated by the force they produce. Shakers vary in size

and force from baseball-sized systems with six pounds of force to SUV-

sized tables. The largest ones are capable of generating 65,000 pounds

force and are used to vibrate satellites and other large structures.

Figure 9. Mechanical vibrators are used in laboratory measurementsand vary in size from small to very large systems.

4

Shakers connect to structures in three ways: by means of a thin metal

rod named a stinger; by placing the structure on a table mounted on

the top of the shaker; or by a slip table that is built onto the shaker

and vibrates in the horizontal direction. In most cases, an

accelerometer is mounted on the structure, near the attachment point

to the shaker, to measure the driving acceleration levels. In some

cases, a load cell on the stinger measures the excitation force.

To drive a shaker a shaker controller is used. The controller is an electronic

device that generates carefully controlled electronic signals, amplifies

them and converts them the excitation acceleration signal. The different

types of vibration profiles include random, burst random and chirp.

A random profile creates a random vibration that includes a broad range

of frequencies. Getting useful results with a random signal requires the

application of a spectral window and data averaging. One advantage of

random vibration is that it is possible to concentrate the excitation energy

at the specific frequencies that will yield optimal vibration measurements.

Burst random consists of a short period of random vibration, followed by

a short period of no excitation. The on/off periods can be set such that the

vibration of the structure dissipates by the end of the off period. This

eliminates the need for windowing because the excitation and response

are periodic. Burst random gives more accurate amplitude and damping

measurements than a random waveform.

Chirp vibration is a short profile that consists of a sine tone that starts at a

low frequency and quickly sweeps to a high frequency. The time of a sweep

is usually one second or less. After each sweep, there is a quiet zone; then

the chirp repeats over and over again. The quiet zone is timed to allow the

structural response to damp out before the end of the data acquisition

frame. This ensures that the excitation and response are periodic in the time

window. The advantage of chirp vibration is that it excites all frequencies

and is periodic. By synchronizing the sampling rate of the signal analyzer

with the chirp signal, the need for windowing is eliminated. Chirp vibration

also yields a better signal to noise ratio than random excitation.

Figure 10. Vibration profiles used by a mechanical shaker to excitestructure for modal analysis including random (bottom left column),burst random (top) and chirp (bottom).

Measurements: FRFs, Coherence, APS

Once vibration is induced, the goal is to measure it. Normally, this is done

by placing accelerometers on the structure and recording the responses

with a signal analyzer. An accelerometer is an electronic sensor that senses

acceleration and outputs a voltage proportional to the acceleration signal.

A signal analyzer is an instrument that records the signals and computes

the frequency domain data.

The number of measurement points needed for a particular structure is an

important consideration in data acquisition for modal analysis. Too many

points will result in an unnecessarily large data set and wasted time. Too

few points will result in a poor representation of the structure and may not

capture the needed mode shapes. Some judgment must be made as to

the important mode shapes and then the number of points chosen that can

accurately represent the structure’s vibration for these mode shapes.

The most common signal types used in modal analysis are Auto Power

Spectrum (APS), Frequency Response Functions (FRFs) and Coherence.

APS is computed from the FFT by squaring and averaging many FFTs over

time. When the FFT is squared it is transformed into a real signal and the

phase information is lost, leaving only the magnitude data.

Frequency Response Function (FRF) is computed from two signals. The FRF

is also often referred to as by the term “transfer function.” The FRF

describes the level of one signal relative to another signal verses frequency.

In modal analysis, it measures the vibration response of the structure

5

relative to the force input of the impact hammer or shaker. An FRF is a

complex signal with both magnitude and phase information.

Coherence is related to the FRF and it indicates what portion of one signal

is correlated with a second signal. It varies from zero to one and is a

function of frequency. In modal analysis, it is used to judge the quality of a

measurement. A good impact produces a vibration response that is

perfectly correlated with the impact, indicated by a coherence graph that is

near one over the entire frequency range. If there is some other source of

vibration, or noise, or the hammer is not exciting the entire frequency

range, then the coherence plot will drop below one in the affected

frequency ranges. Coherence should be monitored during data acquisition

to ensure that the data is valid. The coherence should be close to one at a

resonant frequency. However, it is normal for coherence to be very low at

an anti-resonance, or structural node, where the vibration response is very

low as shown at about 800 Hz in Figure 12.

Figure 11. Frequency response function with magnitude (top) andphase (bottom).

Figure 12. Coherence function shows the quality of the FRF data.

Averaging

Averaging improves the quality of measurements. Averaging applies

to either the frequency or time domain. Frequency domain averaging

uses multiple data blocks to “smooth” the measurements. Two

methods are typically used for averaging: in a linear average, all data

blocks have the same weight; in exponential weighting, the last data

block has the most weight and the first has the least. Averaging acts

to improve the estimate of the mean value at each frequency point and

reduce the variance in the measurement. Time domain averaging is

useful to suppress background noise when repetitive signals are

measured. An impact test is a good example of a test with repetitive

signals. Both the force and acceleration signals are the same for each

measurement. However, if the trigger point is not reliable (due the

presence of high background noise or other problems) the signals

themselves may average away.

Frequency domain averaging is the most frequently used type of averaging

even for impact testing. Figure 13 shows an example of the effect of

frequency domain averaging on vibration resulting from excitation by a

random signal. The top pane shows the spectra after the first frame; the

middle pane shows the spectra after 10 averages; the bottom is after 100

averages. The variance in the spectrum is reduced as more averages are

computed to give a “smoother” spectrum.

Figure 13. Averaging reduces variance in the measurement resultingin a smoother spectrum.

6

It is necessary to use judgment to determine the number of averages to

use in each application. The factors to consider include the randomness

of the signal being measured, the quality of the results needed, and the

length of time required for acquisition of each data frame. A rule of

thumb is to use 32-64 averages for random-type signals and 4 to 8

averages for impact-type signals.

Triggering

Triggering is a technique that makes the analyzer wait to start capturing

data until a triggering event (such as an impact hammer blow) occurs. A

trigger can be set so that data acquisition and processing will not start until

a specified voltage level is detected in an input channel. Either a manual

or automatic arm mode can be used. Manual arming requires an operator

action to activate the trigger each time, after a trigger event, to capture a

new data frame. This mode is used to prevent a faulty signal, such an

intermittent contact caused by a loose cable connector, from causing

a data capture before the real event. Automatic triggering rearms the

trigger after each impact. In this case, the test structure can be struck

with the hammer many times in succession and the data acquired

and averaged without interaction with the signal analyzer. Another

important trigger setup parameter is the pre-trigger. It is used to

capture data immediately before the trigger event occurs. This

feature ensures that you capture the entire waveform.

Figure 14. Software interface for trigger setup.

Windowing

Windowing is necessary when you are computing FFTs for a signal

that is not periodic in the time block. Windowing is always necessary

when you use a shaker to excite the system with broad band noise.

When the FFT of a non periodic signal is computed, the FFT suffers

from ‘leakage.’ Leakage is the effect of the signal energy smearing

out over a wide frequency range instead of staying concentrated in a

narrow frequency range as it does with a periodic signal. Since most

signals are not periodic in the data-block time period, you must

applied windowing to force them to be periodic.

A windowing function is shaped so that it is exactly zero at the beginning

and end of the data block and has some special shape in between. Then

this function is multiplied with the time data block to force the signal to be

periodic. A special window-function weighting factor must also be applied

to recover the correct FFTsignal level after windowing. Figure 15 shows the

effect of applying a Hanning window to a pure sine tone. The left top graph

is a sine tone that is perfectly periodic in the time window. The FFT (left-

bottom) shows no leakage; it is narrow and has a peak magnitude of one,

which represents the magnitude of the sine wave. The middle-top plot

shows a sine tone that is not periodic in the time window, resulting in

leakage in the FFT (middle-bottom). The leakage reduces the height of the

peak and widens the base. Applying a Hanning window (top-right) reduces

the leakage in the FFT (bottom-right).

Figure 15. A Hanning window (far right) reduces the effect of leakageon a sine wave that is not periodic in the data frame time. Thespectrum on the left show the results with a Hanning window appliedversus un-windowed data in the spectrum shown in the middle.

Leakage is easy to understand with pure sine tones. However, it also

affects measurements with all other types of waveforms. Figure 16 shows

a Frequency Response Function (FRF) with and without a window

(Hanning). Here the energy smearing effect of leakage is most evident in

regions where there is a deep trough. Leakage can also affect accuracy of

the amplitude and frequency readings as with sine waveforms.

7

Figure 16. Frequency response function with and without a FFT window.

When using an impact hammer to excite the structure, the time block is

made just long enough to allow all the measured vibration to dissipate.

Since the signal starts and ends at zero, no windowing is needed. This

provides the most accurate amplitude and damping results. When a very

lightly damped structure continues to ring for a very long time period or

when some background noise is present, then a special windowing

function called the exponential window is applied. This function, shown in

Figure 17, has two parts: the pre-window at the beginning of the time

frame, and the exponential window. The pre-window includes a hold-off

period that eliminates any noise before the impact. The exponential

window applies an exponential decay that forces the response data to zero

by the end of the frame; this guarantees a periodic signal. When using the

exponential window, however, be aware that the result will overestimate

the damping of the structure because the windowing function artificially

damps the signal in a shortened time. Figure 18 shows the time response

of a structure without the window in the top frame. Note that the vibration

has not died out at the end of the time record. The bottom frame shows the

results of adding the exponential window. The vibrations are forced to zero

at the end of the time record by the window.

Figure 17. Exponential widow function used for modal analysis withimpact hammer excitation.

Figure 18. Time response of lightly damped structure withoutexponential window (top) and with window (bottom).

Enhancing Measurement Resolution

Frequency resolution (or spacing between frequency lines) is an important

consideration in modal analysis measurements. When resonant

frequencies are close together, a higher resolution is required to accurately

determine the frequency and damping of the two peaks.

There are two methods for increasing frequency resolution: increasing the

frame size, and using FFT zoom. The frequency resolution is

determined by the number of points in the time frame; more points in

the time record result in more frequency lines. Increasing the number

of points in the time record gives a finer frequency resolution. The

drawback is that a longer time frame takes longer to acquire, thus

increasing the overall time required for the measurement. This is

especially noticeable when the frequency span is low (below 50 Hz).

The second method for increasing frequency resolution is to use FFT

zoom. This technique uses a special algorithm to compute the

spectrum within a frequency band that does not start from zero.

(When FFT zoom is not used, standard “baseband” spectra start at

zero.) The signal analyzer has settings for the center frequency,

number of frequency lines and the span. Since the same number of

frequency lines is used over a narrow frequency span, the spectrum

resolution is much finer than for a baseband measurement.

Figure 19 shows a comparison of a frequency response function of a

structure with different measurement resolutions. The first

measurement has the standard 400 frequency lines. The broad

hump near 90 Hz is likely a pair of closely spaced resonant

8

frequencies. Due to the overlapping, the amplitude and damping

cannot be accurately determined with this measurement. In the

second measurement, the number of lines has increased to 1600.

Now the closely spaced peaks are clear. The third measurement used

FFT zoom with a span of 300 Hz and a center frequency of 200 Hz.

This gives the finest frequency resolution of all. Note that the FFT

zoom spectrum does not show any data below 50 Hz because it is not

a baseband spectrum.

Figure 19. Comparison of a spectrum made with 400 and 1600 linesand with FFT zoom, illustrating enhanced measurement resolution.

Signal Quality – Overload and Double Hits

Signal quality is a key consideration in modal data acquisition. Failure to

monitor the quality of the data during acquisition, can give modal analysis

results that are erroneous or invalid. Monitoring the coherence function is

the first step in judging signal quality. If the coherence is poor, it is vital to

take steps to improve it before collecting data.

Other problems that adversely affect signal quality are overload and

double hits by the impact hammer. An overload occurs when the signal

from the accelerometer or impact hammer exceeds the voltage range of the

input channel on the signal analyzer. For example, if the voltage range is

set to 1.0 volt on the signal analyzer, and a strong impact by the hammer

creates a voltage of 1.5 volts, the input channel will overload and the

voltage signal will be distorted. Most signal analyzers provide an alarm to

indicate overload. The data from an overloaded signal are completely

invalid. You should discard them and repeat the test after taking steps to

eliminate the overload. Such steps include reducing the force of the

impact, increasing the voltage range on the signal analyzer, or using an

accelerometer or impact hammer with lower sensitivity. Most signal

analyzer software provides an option to automatically discard data blocks

that include overloads.

A double hit occurs when the impact hammer hits the structure and

then the structure rebounds into the hammer tip. The second impact

may be only milliseconds after the first and is easy to miss on the data

display. A double impact will also produce invalid data. You should

discard the results and repeat the test. You can detect double hits by

viewing a time trace that shows the impact hammer’s force time

history during data acquisition.

Figure 20. An impact hammer double hit can be seen in the forceversus time plot; double hits degrade the quality of the FRFMeasurements.

Data Labeling and Auto-Incrementing

Modal analysis data acquisition consists of measuring the vibration

response at many points on the structure. This usually results in a very

large data set. After acquiring the data, it is imported into a modal

analysis package and each measurement associated with a point on the

structure. Assigning the data to points on the structure can be a tedious

process. Many signal analyzers include a feature that automatically labels

each data point when the data is collected and saved. The label includes

information about the point number and the orientation of the

measurement. Orientation is recorded relative to some assigned axis

system such as x, y, z. The modal analysis software can use this label to

automatically assign the data to the correct points on the structure. Auto-

incrementing is a feature that automatically increments the data label

after every average; this allows the test engineer to move around the

structure with the impact hammer, proceeding from point to point without

the need to interact and operate the signal analyzer after every impact.

9

Figure 21. Modal coordinates can be automatically incremented withsoftware.

Data Export

After acquiring and saving a complete data set, the next step is to export it

to modal analysis software. The signal analyzer must save the data in a

format that the modal analysis software can read. Since the data set can

be very large, it is not convenient or efficient to perform any manual editing

of the data file. Most signal analyzers include options to export data in a

format that is readable by most popular modal analysis software packages.

A special file format named the universal file format (UFF) is also available.

You can use it to export data between most software packages.

Visualization

After acquiring data and exporting it to a modal analysis package, the

next steps are to identify the resonance frequencies, construct the

geometric model of the structure, extract the modal parameters from

the data, and interpret the results by viewing the animated mode

shapes. Several popular modal analysis software packages are

available, and each has a different interface. However, all of them

have the basic structure described here.

Identifying the Resonance Frequencies

Most modal analysis software begins by identifying the resonance

frequencies of the structure. This can be very simple if the structure

has only a few resonance frequencies separated by a large frequency

band; it can be more difficult if there are several resonance

frequencies that are close or overlapping in the frequency spectrum.

The damping of each resonance is another parameter of interest.

Damping relates to the sharpness of the resonance peak.

Most modal analysis software includes tools that automatically identify the

resonance frequencies and damping from the FRF data. These tools use

different methods; the most common is quadrature picking, which

analyzes the imaginary part of the FRF data to find a peak. A resonance will

normally appear as a peak in the imaginary part of the FRF, so quadrature

picking simplifies peak detection. The phase is indicated by a positive or

negative peak as shown in Figure 22.

Figure 22. Imaginary part of frequency response function measuredfrom a beam.

When two or more resonance frequencies overlap, a special technique

called “curve fitting” is applied. This technique is also useful when a

resonance frequency has heavy damping; but in this case, the peak is not

the best estimate of the resonant frequency. Curve fitting compares a

frequency band of data from the measured FRF data to a mathematical

model of a resonance and computes parameters that fit the numerical

model to the measured data. When the two agree, the software saves the

parameters that give the best estimate of the resonance frequencies.

Figure 23. Curve fit interface of the ME’scope modal analysis package.

After identifying each resonance frequency, modal analysis

software examines the FRFs of every measurement point in the

data set at the resonance frequency to compute the mode shape.

Software determines the amplitude and phase of the FRF at the

resonance frequency for every point on the structure.

Creating the Geometric Model

The next step is to create a geometric model of the structure. The model

consists of points connected by lines in an arrangement that appears

similar to the shape of the structure. Most modal analysis software

includes tools for generating basic shapes such as a row of points to

represent a beam, a rectangular array to represent a plate, a cylinder to

represent a tube, etc. The simple shapes can be combined to form more

complex shapes. The model can be very simple or very complex depending

on the level of precision needed from the results. For example, a simple

beam can be represented by a few points sufficient to visualize the first few

mode shapes. However, a complex shape such as a satellite dish requires

many more points for accurate representation of the structure.

Figure 24. Simple beam model (left) and complex satellite dishmodel (right).

The number of modes also influences the geometric model. Modes

related to the lower resonant frequencies tend to have simple mode

shapes; they can be readily visualized with a few points. Modes related

to higher resonant frequencies can have more complex mode shapes;

their models may require finer resolution with more points.

Applying the Measured Data

The next step is to apply the measured data to the geometrical model.

Spatial points connected by lines define the structure’s model. The

vibration response of the structure is measured at the points represented

on the model. Then the measured data are associated with the points on

the model taking care to assure the correct orientation for all points.

Most software includes a tool for assigning the FRF data to points on the

structure. This task is done either manually by picking points on the

structure, or automatically using the labels from the FRF data.

Not every point on the structure must have a measured FRF. The software

can interpolate between points. A beam may have 5 measured FRF points,

and the model may have 10 points, with one extra point between every

measurement point. The software will then compute the modal amplitude

of the interpolated points by analyzing the nearby measured points. A

model with more points may look better than one with fewer points.

Interpreting the Results

The final step is to interpret the results. Animated mode shapes can now

be generated for the model geometry. The user identifies the resonant

frequency of interest, and then the software computes and displays the

model in a deformed mode shape. Users can heighten the level of

deformation to amplify the mode shape. Users can also rotate the model

to view it from the best angle for understanding the mode shape.

Many graphical tools aid in the visualizing the mode shape, including a

colormap that indicates the magnitude of the modal deformation with

different colors. Vectors can draw arrows from the undeformed position to

the deformed position of the model. Mode shape animation draws the

model first in the undeformed position, and then deformed a small

percentage, then a little more, and again and again until the model is in the

fully deformed shape. These images are flashed on the screen for a short

period creating the effect of motion. All these tools give the user the ability

to quickly understand the nature of the mode shapes.

Case Study

The following case study presents the data acquisition and modal analysis

of the muffler and tail pipe section shown in Figure 25. The structure was

suspended on a frame using bungee cords to isolate it from the ground.

Figure 26 shows how the pattern used to mark the measurement points.

10

11

Figure 25. Muffler and tailpipe section mounted by bungee cords.

Figure 26. Measuring point schematic diagram.

Data was collected using an impact hammer and accelerometer. The

accelerometer was fixed in one location using wax and the impact

hammer roved from point to point to make each FRF measurement. An

LDS-Dactron Photon Dynamic Signal Analyzer was used to acquire the

data. Survey test measurements determined that the first few

resonance frequencies were all below 400 Hz; the analyzer span was

set to 1000 Hz. Review of the structure’s vibration versus time graphs

indicated that the vibrations damped out in less than 0.1 seconds; this

led to selection of a time-record length of 400 ms. Averaging was set

to be 5 linear averages; the hammer force signal was used as the

trigger event with a pre-trigger setting that captured data starting just

before the hammer impacted on the structure.

Figure 27 shows the test screen displays used during data acquisition.

The software interface was set to show the measured FRF, coherence

and force, and acceleration versus time. These displays monitor the

quality of the data during acquisition. The modal coordinates window

was set to display the current measuring point ID number and axis and

to update the point numbers with the auto-incrementing feature. The

Channel Status bar indictor as set to show the voltage level of the

inputs and indicates overloads.

At each measurement point on the structure five hammer blows were

made and these measurements were averaged. This process resulted in a

set of 30 averaged FRF measurements, which were saved to disk in a UFF

data format, and then imported into the ME’scope modal analysis package.

Figure 27. The test screen displays on the PhotonAnalyzer during the measurement of the exhaust pipefrequency response functions.

LDS Test and Measurement Ltd.

Heath Works, Baldock Road,Royston, Herts, SG8 5BQ

Phone: +44 1763 255 255E-Mail: info-uk@lds.spx.com

LDS Test and Measurement

8551 Research Way, M/S 140,Middleton, WI 53562 USA

Phone: +1 (608)821-6600E-Mail: info-us@lds.spx.com

LDS Test and Measurement GmbH

Freisinger Straße 32D-85737 Ismaning

Telefon: +49 89 969 89-180E-Mail: info-de@lds.spx.com

LDS Test and Measurement SARL

9 Avenue du Canada – BP 221 F-91942 Courtaboeuf

Téléphone: +33 (0)164864545E-Mail: info-fr@lds.spx.com

LDS Test and Measurement Ltd.

China Head Office, Room 2912 Jing Guang Centre Beijing, China 100020

Phone: +86 10 6597 4006 E-Mail: info-cn@lds.spx.com

www.lds-group.com

In ME’scope a geometrical model was generated as shown in Figure 28.

The geometry is similar, but not exactly identical to the actual structure. For

example, the muffler is modeled as a circular cylinder rather than the oval

cylinder shown in Figure 25. This shape is easier to generate in the

software. Generating the more complex shape takes additional time but

does not help visualize the first few modes.

Figure 28. Geometric model of muffler and tail pipe generated in theME’scope software.

The labels created by the RT Pro software automatically apply the data

to the appropriate points on the structure. The curve fit tools identify

the first and second resonant frequencies; the computer-generated

mode shapes appear in Figure 29. The side view in the lower right

shows the best view of the mode shape. It is similar to an ‘S’ shape

with maximum deflections at 1/4 and 3/4 length and zero deflection

near the middle. This is the classical mode shape of a beam which

illustrates how understanding theoretical vibration response of simple

structures often applies to more complicated structures.

These results could identify critical points on the muffler that are subject to

fatigue or failure. Possible modifications to the structure include changing

the cross-sectional properties, adding stiffeners or using damping

materials. This data could also suggest changing the mounting points of

the muffler to the vehicle. This type of analysis typically starts with a simple

model to identify areas of concern. To verify the need for design

refinements that require additional time and effort, a more refined model

with more measurement points might be used.

Conclusions

Modal analysis is a powerful tool for solving vibration problems. It

identifies the modal parameters of resonant frequencies, damping and

mode shapes. Theoretical modal analysis uses a mathematical model of

the structure and experimental modal analysis uses data that is measured

from a physical structure. Experimental modal analysis uses a two-step

process. The first step consists of acquisition of frequency domain data.

The second step consists of visualization with software that applies the

measured data to a geometrical model of the structure. The resonant

frequencies, mode shapes and damping results can guide modifications to

the structure’s design to suppress vibration, or suggest changes to the

driving function to avoid exciting the resonances.

Figure 29. First mode shape with deformed colormap.

References

Inman, Daniel J., “Engineering Vibrations, Second Edition,” Prentice

Hall, New Jersey, 2001.

12