Think design modifications can only be made on Finite Element models? Think again…!
After performing an experimental modal analysis and calculating a set of modes, each mode has a mass and stiffness matrix that can be modified.
Simcenter Testlab (formerly called LMS Test.Lab) Modal Analysis Modification Prediction can be used to:
After creating a group of modifications, a new set of mode shapes and modal frequencies is calculated that incorporates the changes.
Spring-Damper and Mass Modification Background
Consider a single degree of freedom system, consisting of:
The natural frequency (wn) is equal to the square root of the stiffness over the mass as shown in Figure 1.
A modal frequency can be increased by:
This holds true for all structures, even more complicated ones.
A ‘Spring-damper’ modification can be used to alter the stiffness between two points as shown in Figure 2.
By increasing the stiffness of the spring, the modal frequency will shift higher as shown in Figure 3.
How would increasing stiffness address vibration issues? For example, if vibration from driving on rough road ranged from 1 to 20 Hz, increasing the first body modes beyond 20 Hz would reduce vibration experienced by the driver.
In addition to the stiffness, the damping can also be changed.
Tuned Absorber Background
A tuned absorber is a secondary mass-spring system that is added to an existing mode as shown in Figure 4.
A tuned absorber takes the original frequency of the original system and divides it into two modes. The frequency of the first mode is lower than the original system. The frequency of the second mode is higher than the original system as shown in Figure 5.
The mode shape of the lower frequency would have both the original system mass (m1) and the tuned absorber mass (m2) move back and forth in phase. The two masses would move back and forth out of phase in the higher frequency mode. This is illustrated in Figure 6. If the tuned absorber mass and stiffness is carefully selected, the motion on the original system can be forced to zero by the absorber.
How can a tuned absorber be used to abate a noise and vibration issue? Consider a vehicle where the combustion frequency of engine idle excites a bending mode of the steering wheel column. A tuned absorber could be placed on the end of the steering wheel. This would place one mode of vibration at a frequency lower than the idle which would never be excited. The higher mode could be placed at an engine combustion frequency that the vehicle does not commonly operate at, like 30 mph.
Tuned absorbers are useful when an existing mass can be used. For example, the airbag module at the end of the steering wheel is an existing mass that could be sprung to create a tuned absorber. This modification would not add mass to the overall vehicle (which would have an adverse affect on fuel efficiency). It might also be a cheaper modification than stiffening the steering column to avoid the resonant situation.
When using experimental modes for modification prediction, the following should be considered:
Getting Started with Simcenter Testlab Modification Prediction
Under “Tools -> Add-in” from the main menu, select “Modification Prediction”. If using Simcenter Testlab tokens, it requires 23 tokens total (Figure 7).
A new worksheet called ‘Modification Prediction’ appears at the bottom as shown in Figure 8.
There are two minor worksheets at the top of the ‘Modification Prediction’ worksheet:
Select a set of modes for modification in the upper left corner of the ‘Modification Prediction’ worksheet. Drag and drop modal frequencies over the geometry to view the shape as shown in Figure 9.
Viewing the mode shape aids in deciding appropriate modifications to alter the modal frequency.
Making a Modification: Spring-Damper
Choose a modification of interest. For example, this vehicle body has a torsion mode as shown in Figure 10. Adding additional stiffness around the windshield can make the torsion mode frequency higher.
To add a stiffener, select ‘Add Spring-Damper’ at the bottom of the screen as shown in Figure 11.
In the ‘Add Spring Damper’ menu, define two connection points and a spring constant value. By default, with the "According to connection line" setting, the XX stiffness is added axially between the two points as shown in Figure 12. Damping can also be added.
It is not necessary to type the node names into the ‘Attachment point’ menu fields. You can simply click on the node in the geometry and it will fill into the ‘Attachment point’ automatically, as shown in Figure 13. Press the ‘Apply’ button when finished.
Multiple modifications can be made. In this case, two ‘Spring-damper’ elements were added to increase the torsion mode of the vehicle as shown in Figure 14.
Click on the ‘Predict Modes’ tab at the top of the ‘Modification Prediction’ worksheet as shown in Figure 15. Press the ‘Calculate’ button to create a new set of modes, with the modifications applied.
The Frequency Response Functions (FRFs) of on the points of interest are displayed. Green is from the modified mode set, while red is from the original mode set.
Making a Modification: Tuned-Absorber
At 27.39 Hz, there is a roof pumping mode as shown in Figure 16. A tuned absorber can be applied to this mode.
Click on the ‘List Modifications’ minor worksheet. If desired, eliminate any previous modifications by highlighting the entire row and pressing the ‘Delete’ button as shown in Figure 17.
Click on the ‘Add Tuned Absorber’ button.
In the tuned absorber menu (Figure 18):
Press ‘Predict Modes’ tab to create a new set of modified modes. Just above the ‘Calculate’ button, on the middle left, enter text in the ‘Processing data’ field to name the new data set. Press the ‘Calculate’ button to apply the tuned absorber as shown in Figure 19.
The new modes and their frequencies are listed in the lower left of the screen. The FRF with the red line is based on the original set of modes. The FRF with the green line includes the tuned absorber modification.
Tuned Absorber Trivia
From a dynamics point of view, skyscrapers are equivalent to long metal beams coming out of the ground. They have low frequency modes of vibration excited by the wind. The top of a skyscraper can move many feet. Many have tuned absorbers to help reduce the movement/vibration.
The Taipei 101 skyscraper contains the world's largest and heaviest tuned mass dampers, at 660 metric tons (730 short tons) as shown in Figure 20.
The tuned absorber is viewable by the public on an indoor observation deck at the top of the skyscraper. It cost an estimated $4 million to build.
Use Simcenter Testlab Modal Analysis Modification Prediction to simulate product design modifications on experimental modal analysis results. The following modifications can be done:
After creating a new mode set, it is interesting to use the Modal Assurance Criterion (MAC) to compare the original set of modes to the modified modes as shown in Figure 21.
Using the MAC analysis, it is possible to see the effects of modifications on modal frequencies and mode shapes. In the MAC table of Figure 21, red indicates modes that are 100% alike.