Simcenter Testing Solutions Modal Stabilization Diagram Tips

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A stabilization diagram is used in modal curvefitting to determine modes from a set of measured  Frequency Response Functions (FRFs).  The stabilization diagram provides a visual guide to what modes are present within the FRF data set.  This is usually indicated by a column of “s” symbols (“s” short for stable) aligned with a peak in a FRF summation as shown in Figure 1.
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Figure 1: A column of “s” letters corresponding to a peak in the stabilization diagram, part of the modal curvefitting processing, strongly indicates the presence of mode in the test structure.
However, there is not always a single strong column of “s” (which indicate the mode is very repeatable) or clear peaks in the FRF summation in every stabilization diagram.  

There can be several reasons why this occurs.  This article discusses some of the underlying reasons why stabilization diagrams are not always perfectly clear, and what can be done to extract meaningful results in these situations:
  1. Stabilization Diagram Background
  2. Local versus Global Modes: Structures which contain smaller components can have localized modes that do not present well in the stabilization diagram. 
  3. Exciter Direction and Location: If the modal exciter is not well placed to excite the modes of a structure, the stabilization diagram clarity suffers.
  4. Mass Shifting: When multiple measurements must be performed that require accelerometer locations to be moved, inconsistencies are created in the FRF data set that look like multiple modes at similar frequencies rather than a single mode.

1. Stabilization Diagram Background

The stabilization diagram is used as part of the modal curvefitting process to aid an operator to determine the modes of a test structure based on measured Frequency Response Function (FRF) data.

Simcenter Testlab software assumes (i.e., guesses) that a certain number of modes are present in the structure and determines the frequency and damping for the modes that best match the FRF data.  

The software does not know the real number of modes in the structure, so it starts by assuming one mode and incrementing to a number of modes set by the operator. The result of this process, called a stabilization diagram, is shown in Figure 2.
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Figure 2: The letters on the stabilization indicate how repeatable a modal solution (frequency, damping, etc) are when assuming a certain number of modes in the FRF data (left vertical axis).  The letter “s” indicated “stable” while “o” is a not previously found solution from the previous step.

When the same frequency and damping (within a tight tolerance) repeat themselves between increments, the letter “s” is used to indicate the solution is repeatable or stable.  Ideally, a column of letters “s” will appear to give the user a strong indication of a mode within the FRF data set.  Only one “s” needs to be selected from a column since the solution is repeatable.

Measurement function(s) can be overlaid on the diagram to help aid in the selection of letters.  This function could be a single FRF summation, or any/all of the individual FRF functions as shown in Figure 3:
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Figure 3: Left, Top – Stabilization with single summation overlaid, Right, Bottom – Stabilization with all individual measurements overlaid.
The FRF summation is just a visual aide to help interpret the letters being presented. All of the individual FRFs are used in the calculation of the modal estimates (ie, the letters) shown in the stabilization diagram.  The summation just graphically aids in interpreting the letter selection.

The FRF summation calculated in the Simcenter Testlab software is “normalized”.  It is divided by number of FRFs used in the sum.  

More background on the process of modal curvefitting in knowledge article: Getting Started with Modal Curvefitting.

The strong column of “s” letters and corresponding peak are strong indicators of the existence of a mode of vibration in the structure.  However, in a real life test, a strong column of letters may not be present nor a peak in the summation.  The cause and possible solutions for some of these situations are covered in the next sections.

2. Local versus Global Modes

In the stabilization diagram in Figure 4 below, there is a column of letters where there is no frequency peak:
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Figure 4: Stabilization diagram has a column of letters with no corresponding peak in the FRF summation to indicate the presence of the mode.

Why would the stabilization diagram indicate a mode via letters, but no peak show in the FRF summation? One reason is that the test structure contains small physical components.  Consider the structure shown in Figure 5.  
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Figure 5: Structure consisting of global components (body and rails) and local components (steering wheel, axle, engine, subframe, etc).

This structure has several distinct sub-components including a steering wheel, engine, axle, subframe, etc.

A complex structure like this can have global and local modes as shown in Figure 6
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Figure 6: Global body bending mode (left) versus local lateral steering wheel mode (right).

Global modes are present in almost every FRF measured on the structure.  Local modes will only be present in a subset of FRF measurement locations. This is why a FRF summation based on all FRFs may not show a peak due to the local mode of a component.  The global modes “wash out” the local modes in the FRF summation.

It is useful to analyze the FRFs based on individual components instead of all FRFs.  In the “Modal Data Selection” worksheet of Simcenter Testlab Modal Analysis, there is a field called “Point filter” (Figure 7) that can be used for analyze/view:
  • All FRF data: Leave the “Point filter” field blank.
  • Component only FRF data: The component name (or part of a component name) can be entered in this field.
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Figure 7: Left – Point filter is blank, all 375 FRFs are selected, Middle – Point filter set to “eng” selects 18 FRFs, Right – Point filter set to “whel” selects 15 FRFs.

It is then easy to sum the FRFs for each “Point filter” option.   This is done by switching to the “Polymax” curvefitter worksheet.  Press the “Save Sum/MIF” button and provide a name as shown in Figure 8 below:
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Figure 8: After filtering on “eng” in the “Modal Data Selection” worksheet, a FRF Sum can be created for the engine FRFs in the “Polymax” worksheet.

The sums, stored in the project, can be placed over the stabilization diagram using the “Data Explorer” icon at the top of the screen as shown in Figure 9.
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Figure 9: Click on the “Data Explorer” icon.  Find the sum in the “Polymax Band” folder and drag it into the display.

After opening the Data Explorer, drop the sum on the Stabilization Diagram.

In this case, the sum of the FRFs from the engine locations (green) shows a peak that the FRF summations of the steering wheel (red) and summation of all FRFs (blue) do not (Figure 10).
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Figure 10: Engine FRF summation (green) shows peak that other summations (red and blue) do not.

With a peak now showing in the summation of the engine FRFs, there is higher confidence that the column of letters corresponds to a mode.  It is also highly likely that his corresponds to a local mode of the engine as well.

Calculating FRF sums based on components is helpful in identifying modes with a more certainty. The peaks in the summation of an individual component can indicate the local modes of the component when the global summation does not. 

As mentioned previously, the FRF summation calculated in the Simcenter Testlab software is “normalized”.  It is divided by number of FRFs used in the sum.  This allows the sums from different components to be overlaid on the same scale.  If the sum was not divided by the number of measurements, there could be an order of magnitude difference in the amplitudes of the sums of different components.

3.  Exciter Direction

Each mode of a structure can be quite different.  The mode shapes can have a natural motion that can be dominant in different directions like those shown in Figure 11.
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Figure 11: Left – Twist mode with lots of side to side motion, Right – Mode with primarily vertical motion. 

If the modal exciter is not aligned with the motion of a mode shape, it may not excite the mode fully at that frequency. This is reflected in the FRF data.

Not having the exciter well aligned can manifest itself in the stabilization diagram as shown in Figure 12.
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Figure 12: Stabilization diagram (left – two reference exciters in different directions) has strong column of “s” to indicate a mode while stabilization diagram (right – one reference exciter) does not.

When only one exciter is applied, there is not a clear column of “s” symbols.  When FRFs from a second exciter are introduced, which is applied in the same direction of the mode shape, the mode is in a better position to be identified.  As a result, there is a strong column of “s” symbols.

In an experimental modal test, it is often helpful to have multiple exciters with different orientations.  More about multiple input modal testing in the knowledge article: Simcenter Testlab MIMO FRF Testing.

4. Mass Shifting

Another common situation in modal testing is that there are more points to measure than accelerometers available.  As a result, to do a complete modal test at all desired measurement locations, several measurements are performed where the accelerometers are moved or roved between locations (Figure 13).
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Figure 13: Often in modal testing, accelerometers must be roved between desired measurement locations to make a complete modal test.

This causes small shifts in the mass distribution of the test object due to the accelerometers being in different positions. Because the natural frequency of an object is proportional to the stiffness divided by the mass of the object, the frequency of the modes is different between the FRF measurements.

This shifting phenomenon is often ignored by users who assume the mass of the accelerometer is negligible compared to the total mass of the test object.  This assumption does not work for dynamic modes of a structure.  Many modes are local, with only a fraction of the mass participating.  An accelerometer in the right location (centered on local panel breathing mode) can alter the frequency greatly.

This shift in natural frequency will manifest itself in the stabilization diagram.  Around each mode, there is a cluster of letters rather a single column as seen in Figure 14.
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Figure 14: In a roving accelerometer test, the inconsistencies in natural frequencies cause a cluster of letter symbols at each mode rather than a single column of letter symbols.

If all FRF measurements could be acquired at one time, instead of roving the accelerometers, then the stabilization diagram would show single columns of letters as shown in Figure 15:

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Figure 15: When all data is acquired at once, there is no mass/frequency shifting.  Each mode has a distinct column of letters rather than a cluster of letters. 

Nothing can be done to adjust the FRFs that were already acquired – they will always have inconsistent frequencies.  

To get meaningful mode shapes from the FRF data, a “multi-run modal” solution is available in Simcenter Testlab.  In this approach, each set of acquired FRFs is curvefit separately and the partial mode shapes are combined as shown in Figure 16.
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Figure 16: To overcome frequency inconsistencies due to accelerometer mass shifting, the multi-run modal combines separate curvefits of each individual accelerometer move into a single mode shape.

The multi-run modal approach treats each acquisition that is performed separately, instead of combining them for analysis.  This avoids frequency shift inconsistencies within the data set.  

But having separate analysis files for each acquisition gives only a partial mode shape.  The multi-run analysis combines the partial shapes into one complete mode shape, and it is assigned to a single frequency from one of the analyses performed (user selected).

More information on the multi-run mode approach in this article: Simcenter Testlab: Multi-Run Modal

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