Simcenter Testing Solutions Modal Testing: A Practical Guide

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This article explains some of the key steps involved in performing a modal test, from start to end. 

In an experimental modal, a physical structure is tested, and its modes of vibration are identified (Figure 1).  The modes are identified by natural frequency, damping, and mode shape.
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Figure 1: Left – Modal test setup for an aircraft, Right – Output of modal test is frequency, damping, and mode shape. 

A known input is applied, and the response of the structure is measured. The ratio of the response to the input, a Frequency Response Function, is used to determine the modal properties of the structure. The modal properties are derived from the structure itself, and are ultimately independent of the input and outputs.

From start to finish, there are several key decisions to be made at each step in the process, as shown in Figure 2:

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Figure 2: Key facets of an experimental modal test from setup to execution to analysis.

These steps are covered in this article:

1. Test Setup
    1.1 Boundary Conditions
    1.2 Driving Point Search
    1.3 Force Method: Hammer or Shaker
    1.4 Force Level: Proper Tip and Frequency Range
    1.5 Force Level: Linearity
    1.6 Geometry
2. Test Execution
    2.1 Managing Accelerometers 
    2.2 Mounting Accelerometers: Right-Hand Rule
    2.3 Mounting Accelerometers: Angle
    2.4 Roving Hammer versus Roving Accelerometer
    2.5 Quality Check: FRF and Coherence
3. Post Test
    3.1 Modal Curvefitting
    3.2 Modal Validation: Modal Assurance Criterion
    3.3 Modal Validation: Modal Synthesis
    3.4 Other Post Test Analysis Options

1.    Test Setup

The preparation and setup of a modal test are critical.  The data needs to be acquired in the conditions of interest and must be of high quality.  Mistakes made in the setup of the test will either add extra time in the analysis step, or even worse, cannot be compensated for in the analysis phase and may require retesting.

1.1 Boundary Conditions

What is the objective of test?  The conditions under which the test object is measured are dictated by the test objective.

Consider an “engine cradle” shown in Figure 3.  This is a metal structure that holds an engine in place in a vehicle.  It has attachment locations to the engine and to the body.
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Figure 3: A engine cradle normally attaches to both a body structure and to an engine at the mount locations.
Should the test be performed on the engine cradle by itself?  Or should the engine cradle be attached to an engine and to a body when the test is performed?  This depends on the test objective:
  • Installed Boundary Conditions: Perhaps the dynamic behavior of the entire vehicle needs to be understood.  In this case, the engine cradle will need to be attached to the body structure and to the engine.  Not only should the engine cradle be measured, but the body structure and engine should be measured as well.
  • Free-free Boundary Conditions: To understand the dynamic behavior of the complete vehicle, an analyst might build a finite element simulation model.  Rather than build a model of the entire vehicle at one time, the model could be built in smaller components.  Individual components, like the engine cradle, can be tested and modelled in free-free boundary conditions. After verifying that the dynamic behavior of the free-free component test adequately matches the simulation component, boundary conditions can then be added to the model and understood.
By separating the modelling of the boundary conditions from the dynamics of the individual components, higher accuracy is usually achieved because each part is better understood.  The components can be assembled together with the appropriate boundary conditions.  Because the components were already verified and accurate, the analyst can concentrate on just the boundary conditions, rather than trying to model everything simultaneously.
A free-free boundary condition removes outside influences on a test article by “suspending the object in space”.  In a computer-based model, suspending an object in space is easy, as shown in Figure 2.  For a physical modal test, this is done by suspending the object on soft springs (like elastic cords or airbags) as shown in Figure 4.
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Figure 4: A engine cradle modal test being performed in free-free boundary conditions.
When an object is suspended freely, the first six modes of the test object are typically “rigid body” modes.  In a simulation model, these six modes all occur at zero Hertz.  There are three translational rigid body modes, and three rotational rigid body modes.  In a physical modal test, the modes are never perfectly at zero Hertz. The frequency they occur at depends on how softly the test object is suspended.
An example of a rigid body mode versus a flexible mode is shown in Figure 5.
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Figure 5: Left – One of six rigid body modes at zero Hertz for an engine cradle.  Right – A flexible mode of vibration of an engine cradle.
What is the difference between a rigid and flexible mode of vibration?:
  • Rigid Body - In a rigid body mode of vibration, the object under test does not experience modal deformation.  It vibrates as a single unit on the soft springs that is mounted upon (left side, Figure 5).  
  • Flexible Body - In a flexible mode of vibration, the test object deforms.  For example, it might twist or bend (right side, Figure 5).
When performing a modal test to verify the dynamics of a complex structure, often both free-free and tests with representative boundary conditions are made depending on the objective of the current phase of the project.

Boundary conditions can be different from a lab test versus what is experienced in real life.  For example, the shock absorbers on a car have a certain amount of stiction.  Without overcoming the stiction, the absorber looks like a rigid connection, but it does not behave this way on the road.  For a laboratory test, a shaker operating at low frequency can be made to stroke the absorber to get the right boundary condition.

Sometimes it might be desirable to perform the modal analysis on the test object under representative loads from real operation.  The loads from a single shaker placed on a engine would not represent the loads experienced during wide open throttle. Operational Modal Analysis can be used in this circumstance.

1.2 Driving Point Search

Another decision before a modal test is performed, is to decide where the force excitation will be applied. Ideally, the selected location should easily excite all the modes of the test structure.

This location can be determined via a “driving point” search.  In a driving point search, an impact hammer and accelerometer are roved together over the structure to identify the resonant frequencies of the different parts.  The various measurements are summed to get a complete picture of all the resonant frequencies present.

Some of the results of a driving point survey are shown in Figure 6.
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Figure 6: In a driving point survey, the location that excites all the modes of the structure (green) is the best excitation location for the modal test. Locations that fail to excite all frequencies (red) are to be avoided.

After identifying all the natural frequencies in the structure, the best single excitation location is determined.  The individual driving point FRF measurement that showed all the frequencies is considered the ideal place to use as an input for the complete modal test.

See the article “Driving Point Survey, What’s at Stake?” for more information.

1.3 Force Method: Hammer or Shaker

Generally speaking, the force applied during a laboratory based modal test can come from a shaker or an impact hammer (Figure 7).
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Figure 7: Left – Impact hammers for modal excitation, Middle, Right – Electrodynamic shakers for modal excitation.
When to use a shaker or a hammer?
  • Impact Hammer: An impact hammer takes no setup – just hit the structure at the desired location. It is quick, but the force is uncontrolled.
  • Shaker: A shaker requires careful positioning at the desired force input location which is more time consuming.  However, the force can be precisely controlled, and multiple shakers can be used simultaneously.
Consider exciting the two structures shown in Figure 8.
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Figure 8: Left – Smaller objects can easily be excited by a shaker or hammer, Right – Exciting a large structure with a single impact hammer may not excite the entire structure and can result in non-linear localized behavior.  Using multiple shakers simultaneously can yield better results.
Smaller objects can easily be excited by a shaker or hammer as shown on the left of Figure 8.  When using an impact hammer to excite the large structure on the right of Figure 8, it might be difficult to measure the response on the other side of the structure. The structure is so large that the vibrations die out as they travel across the structure.

To get more response on the other side of the structure, it might be tempting to use a higher force with the hammer by hitting harder.  This may increase the response, but it can also result in non-linear localized behavior at the point of impact.  Using multiple shakers simultaneously, each located on different sides of the structures, can yield better results.

Schematics of a typical impact and shaker modal test are shown in Figure 9.
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Figure 9: Left – Impact hammer modal setup, Right – Shaker modal setup

See the following articles for more information on impact and shaker testing:

1.4 Force Level: Proper Tip and Frequency Range

When performing a modal test, the excitation force must excite the frequency range of interest. 

For shakers, this means entering the desired frequency range in Simcenter Testlab software.  For impact measurements, this can be a bit more challenging.

In an impact hammer measurement, the input tip is in contact with the structure for a very brief time, as shown in Figure 10.
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Figure 10: Right – Brief contact force between impact hammer and structure, Left – The Fourier Transform of a brief event in time is broad in frequency.

In fact, the shorter the contact time between the structure and hammer tip, the more broad in frequency the response.  

Using a hard tip, like a metal, yields a higher frequency range than a soft tip, like rubber (Figure 11).

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Figure 11: Modal impact hammers are usually provided with a set of tips with differing stiffnesses.

Ideally, the tip should be selected so that the energy of the hit excites the frequency range of interest and no more.  It is desirable to have as much input force into the structure over the frequency range of interest, and not “waste” energy in frequencies beyond the range of interest.

In Figure 12, the results of two different tips are compared.
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Figure 12: Top – Metal tip on impact hammer excites higher frequency range.  The input force spectrum (blue) remains at a consistent level over the frequency range of interest.  Coherence (green) values are close to one at resonance, and the FRF (red) is clean. Bottom – Rubber tip on same structure excites lower frequency range. The input force spectrum (blue) is rolloffs over the frequency range of interest.  The FRF (red) is noisy, and the coherence (green) is not close to one, even at resonant frequencies.
Without carefully checking the impact measurement, noisy data with poor coherence could result as shown in Figure 12.

The mass of the hammer head is also a factor in determining how long the hammer and structure stay in contact.  The higher the mass of the hammer head, the longer the contact, and the lower the frequency content.  However, the input force levels are higher with the mass than without it. Impact hammer kits also have optional mass extenders (picture in Figure 11).

For more information, see the article “What modal impact hammer tip to use?”.

1.5 Force Level: Linearity

An implicit assumption in a modal test and the subsequent analysis is that the structural response is linear.

What does a linear response mean?  And what is a nonlinear response?  A force is applied to the test object during the modal test.  If the force was high enough, the object simply breaks!  This would be a nonlinear response.  Easy to imagine that it would be difficult to develop a modal model of the test object if it breaks.

The test object does not need to break to exhibit nonlinear response.  In a linear response, if the force level doubles, the acceleration response should also double.  Apply one Newton of force and get two g’s of acceleration, a linear structure would respond with four g’s when the input force doubles to two Newtons.

But this does not always happen in practice.  There can be nonlinear components, like rubber bushings, loose parts, fluids, etc that cause the relationship between input and output to be nonlinear.

Since the force applied during the test can vary (for example if using random) then it is a good practice to do a linearity check as shown in Figure 13.
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Figure 13: Left – Three different force levels (blue, red, green) are applied to the structure, Right – The Frequency Response Function at a response location due to the three different forces (blue, red, green).  
In a typical linearity check, the intended force level for the test is doubled and halved.  The FRF between a response location and the force is compared.  If the structure is linear, the three FRFs should be identical.  If the frequency of certain peaks shift, or the amplitudes are different, than the structure contains some non-linearities.

What to do if nonlinearity indicated? Some ideas:
  • Run shaker continuously at the higher amplitude. While the shaker is running, search for loose parts and rattles. Eliminate them.
  • Be on the lookout for any part that contains fluid that may slosh.  Eliminate the fluid if possible.
  • Look for parts that may break free or interfere with each other.
  • Run the test at a lower force level that passes the linearity check.
  • Consider a different force type that has constant amplitude.  For example, a sinusoidal type input.
1.6 Geometry

Creating a geometric layout of all points will be tested during the modal campaign is a best done before the test starts.

A geometry is defined by a series of points as shown in Figure 14.  Each point defined by a location co-ordinate in space, and an orientation.  An accelerometer will be placed at this location on the actual test object.
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Figure 14: A series of points, or nodes, (left) where accelerometers will be measured on the aircraft test object (right).
How many points are enough? There are a few considerations:
  • Communicate to an Audience: The results need to be understood by others.  At a minimum, be sure to include enough points so that the object is recognizable to the modal test result recipients.
  • Ground: Testing a component that is tied to ground, so it cannot move?  Might be a good idea to place an accelerometer on that ground and verify that it really does not dynamically move.  Many an analyst has been surprised that what appears to be a solid ground is actually not from a dynamic point of view.    
  • Component: Testing a component that is installed in a larger structure? Be sure to measure on the larger structure, not just the component!  Modes of the larger structure will affect the component.  If measurements are only performed on the component, what appears to be a mode of the component may really be part of a larger mode of the structure.
  • Frequency Range: The higher the frequency range and more modes being measured, the more complex and localized the mode shapes become.  More points are needed to capture these mode shapes fully. If not enough points are measured, the higher frequency mode shapes can look similar to lower frequency mode shapes.  This is called spatial aliasing.

Some empirical tools, like Modal Assurance Criterion (MAC), which is discussed further ahead in the article can also help ensure enough points are acquired.  Software like Simcenter 3D Pretest can use the MAC on a simulation model before the test to optimize the measurement locations.

Need more information?  See the article “Simcenter Testlab Geometry”.

2.    Test Execution

Ideally, all output response locations could be measured at the same time in a modal test.  However, there may be more desired measurement locations than physical  accelerometers available.  In this case, the accelereometers are typically roved over multiple measurement locations.  By applying the reference force at a consistent location while moving the accelerometers, the measured Frequency Response Functions will be phased properly. 

The accelerometer locations, directions, and angles must be recorded properly during this process.

2.1 Managing Accelerometers

When performing a modal test where several locations need to be measured with a limited number of accelerometers, it is helpful to plan accordingly. For example, suppose there are twelve accelerometer locations to be measured, but only two accelerometers available.

These two accelerometers can be roved over the measurement locations as seen in Figure 15.  The points are laid out in an ascending order on both sides of the test object.  A yellow plane of symmetry is shown for illustration purposes.
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Figure 15: Accelerometer measurement locations are laid out in ascending order on two sides of a symmetric test article.
On advantage of this layout is that the points are laid out so that the increment feature can be used to easily update to the next point identification as shown in Figure 16.
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Figure 16: The “Increment” button (bottom) in Simcenter Testlab allows identifications to be easily updated.  The increment can be set to any number to allow for differing amounts of roving accelerometers.

This helps eliminate errors in labelling the data while collecting it.  In Simcenter Testlab, the measurement point identification must match a corresponding node in the geometry.

The layout also reduces how far the accelerometers need to be moved for each measurement as shown in Figure 17.
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Figure 17: The accelerometer layout helps minimize the time to move accelerometers and helps reduce wiring interference.

This helps keep the wires from becoming tangled and minimizes the time for the overall test.

Additional information on these topics: 
2.2 Mounting Accelerometers: Right-Hand Rule

In order to properly animate the modal data, the directions (typically +/- X, Y, Z) must be entered correctly for each measurement channel.

Depending on the orientation that the triaxial accelerometer (accelerometer which measures three directions independently) is mounted onto the structure, only certain combinations of directions are possible.  

This is because the three channels in the accelerometer are in a fixed orientation with respect to each other.  This orientation can be described by the “right-hand rule” which is illustrated in Figure 18.
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Figure 18: By setting the “MultiChannel” field in Simcenter Testlab to “Triax-RH” (upper right), directions entered for a triaxial accelerometer (bottom right) will automatically adhere to the right-hand rule (left).
If the direction of the three channels (+X, +Y, +Z) of the triaxial accelerometer do not match exactly with +X, +Y, +Z of the geometry, then they need to be changed. 

Suppose the Z direction channel of the accelerometer is facing down, rather than up.  One scenario:
  • +Z becomes -Z:  Using the right-hand rule, the thumb would be pointed down and not up.
  • +Y becomes -Y: The middle finger then points rotates from +Y to -Y.
  • +X stays the same: The pointer finger stays in the same orientation.
In this case, the directions are +X, -Y, -Z for the three channels.  An orientation of +X, -Y, +Z is not possible.

Of course, the XYZ of the triaxial accelerometer could even be oriented so XYZ do not align with the XYZ of the geometry! However, the right-hand rule will still apply.

See the article “Cool triaxial accelerometer tips!” for more information.

2.3 Mounting Accelerometers: Angles

Another challenge when mounting an accelerometer on a test article is that mounting surfaces are not always perfectly aligned with an orthogonal co-ordinate system.  Many products have curved surfaces as shown in Figure 19.
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Figure 19: Test objects often have irregularly shaped surfaces (top).  Using small wedges (bottom) to mount the accelerometers to the test object makes it easy to ensure the measurement aligns with the global co-ordinates/orientations.
Curved or irregular surfaces can make it difficult to mount the accelerometer aligned with the test co-ordinate system.  In a single test object, there can be multiple, different mounting angles. A simple workaround is to have an assortment of small angled blocks available that can be used between the test object and accelerometer.   

By using the wedges, the measurements can all be taken in a consistent global set of co-ordinates.

Another possibility in Simcenter Testlab Geometry is to rotate individual accelerometer locations as shown in Figure 20.
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Figure 20: In the Simcenter Testlab Geometry module, individual nodes can be rotated. The last three columns of the node table contain rotation angles which can be applied to individual nodes (circled in red). 
If comparing the test mode shapes to a simulation model, rotating individual nodes may pose some difficulties.  The nodes in a simulation model are not usually individually rotated.  If doing a comparison, it is good to know the orientations used in the simulation model so the measurements can be acquired in the same orientation during the test.

Need more information?  See the article “Simcenter Testlab Geometry”.

2.4 Quality Check: FRF and Coherence

During the measurement, the acquired Frequency Response Functions (FRFs) and corresponding coherence functions should be monitored and checked.  Example measurements are shown in Figure 21.
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Figure 21: During a modal test, the Frequency Response Function (FRF) for each measurement should be checked.  Left – A good FRF measurement has a coherence close to one, Right – A bad FRF measurement is noisy, and has a low coherence.

In Figure 20, two measurements are shown on the right and left side:
  • Left: The coherence function, which indicates the repeatability of the measurements should normally be close to 1 as shown (green, upper).  The FRF should be clean (green, lower).
  • Right: If a problem occurred during the test, for example if an accelerometer cable went bad, the FRF measurements would be noisy as shown on the right side (red, lower). The coherence would not be close to 1, indicating a problem (red, upper).
By catching the bad measurement during the test, the data can be immediately re-acquired after fixing the problem.  Finding bad data during post test analysis after de-instrumenting is much more time consuming to remedy.

Another good practice is to measure the driving point measurement throughout the test.  In a shaker test, this can be done with something like an impedance head that measures both force and acceleration at the shaker input location.  If the test requires multiple measurements, the driving point measurement is an excellent reference.  

For example, if a mode shifted in frequency from the beginning of the test to the end of the test, this can be traced via the driving point FRF for each separate measurement.  Perhaps someone accidently left a coffee cup (a mass that shifts the frequency) on the structure during the measurement campaign.  The exact measurements affected by the coffee cup can be found (hopefully no one leaves a cup on test structure, just using this for an illustration!).

Check out the “What is a Frequency Response Functions (FRF)?” article for more information.

3. Post Test

After the Frequency Response Functions (FRFs) have been acquired, they are analyzed to extract the modal frequencies, dampings, and mode shapes.  This process is called modal curvefitting.

3.1 Modal Curvefitting

In the modal curvefitting process, a mathematical model is made using the acquired FRF data.  The Simcenter Testlab software does mathematical computations to decide the best possible frequencies, damping ratios, and shapes that would explain the FRF data with minimal differences.

It is up to the human analyst to make the final decisions on which frequencies, dampings, etc to keep from the modal curvefitter.  A stabilization diagram of possible choices is presented to the user as a decision-making guide (Figure 22).
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Figure 22: A modal stabilization diagram from Simcenter Testlab.
In the case of Simcenter Testlab, the diagram is presented with letters that represent possible modes of vibration.  The letter “s” indicates a mode that is a stable estimate, no matter how many modes are fit to the data.

For more information, see the articles:

3.2 Modal Validation: Modal Assurance Criterion 

With the modes selected, there are validation tools to help access the reliability of the mode selections.  One of these tools is the Modal Assurance Criterion (MAC).

The Modal Assurance Criterion is used to compare two mode shapes and determine how similar they are.  If the MAC has a value close to one, then the modes have the same shape, while values close to zero indicate that the shapes are different.

An example output of a Modal Assurance Criterion calculation is shown in Figure 23.  A set of nine modes from a modal curvefit are compared to each other.
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Figure 23: Modal Assurance Criterion (MAC) on a set of nine modes from a modal curvefit.  The diagonal of red bars in the center are the same modes compared to themselves, so a value of one is expected.  The off-diagonal terms, which are the MAC values of different modes compared to each other, should be close to zero because the mode shapes are expected to be unique.
Modal Assurance Criterion: Indicates how unique each mode shape that was selected is compare to all others. This can indicate possible problems, for example, if the same mode was accidentally picked twice.  It might also indicate if not enough points were measured during the test, resulting in shapes from different modal frequencies that look the same, but in reality are not.

See the article “Modal Assurance Criterion” for more information.

3.3 Modal Validation: Modal Synthesis

While the Modal Assurance Criterion can indicate if too many modes were selected, the Modal Synthesis can check if any modes were missed during the modal curvefitting process as shown in Figure 24.
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Figure 24: Modal synthesis compares the measured FRF data to a synthesized FRF from the modal curvefit.  It can indicate if there is a low probability that modes were missed (left) or indicate if modes are missing (right) .
Modal synthesis is a process where a FRF is generated from the modes found during modal curvefitting.  This synthesized FRF can be compared to the actual measured FRF to see if there is a good match. 

In Simcenter Testlab, the match is also indicated numerically.  There is a correlation and an error percentage assigned to each synthesized FRF and its corresponding measured FRF.  The error percentage should be as close to zero as possible, whereas the correlation percentage should be as close to 100% as possible.

See the article “Getting Started with Modal Curvefitting” for more information.

3.4    Other Post Test Analysis Options

Some other analysis options include:
  • MLMM - Maximum Likelihood Modal Model can tweak the modal estimates to follow the measured FRFs
  • Mode Shape Expansion - Take test nodes and project onto a CAD or FEA geometry
  • Modification Prediction - Add stiffness, mass, and tuned absorbers to test modal models to predict new modes
Questions?  Email or contact Siemens Support Center.

KB Article ID# KB000043416_EN_US



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