Damping with nonlinear prestressed modal analysis

[meshparts]

Hello,

I’m trying to do a full nonlinear prestressed modal analysis in ANSYS.

The model is basically two plates screwed together by four screws.

So the nonlinearity comes from contact and the damping from friction in the contact.

I’m doing the analysis based on the example from the ANSYS help, see Chapter “3.12. Brake Squeal Analysis”.

The problem is, that I get zero damping judging from the solution output below (real part of damped eigenfrequency is zero):


***** DAMPED FREQUENCIES FROM REDUCED DAMPED EIGENSOLVER *****

MODE COMPLEX FREQUENCY (HERTZ) MODAL DAMPING RATIO

1 0.0000000 7968.4915 j 0.0000000
0.0000000 -7968.4915 j 0.0000000

Now if I list the results…:


***** INDEX OF DATA SETS ON RESULTS FILE *****

SET TIME/FREQ(Damped) TIME/FREQ(Undamped) LOAD STEP SUBSTEP CUMULATIVE
1 0.0000 7968.5 j 8007.5 1 1 1
0.0000 -7968.5 j

… the undamped frequency of 8007.5 Hz is bigger than the imaginary part of the damped frequency of 0.0000+7968.5*j.

So the damping could be: D=acos(7968.5/8007.5)= 0.0987


If my calculations are correct, why is the real part of the damped eigenfrequency zero in the listings?

Has anyone any idea?

Regards
Alexandru Dadalau

 

[seymours2571]

Modal analyses are inherently linear analyses. Non-linearities are not taken into account.

I believe you can simulate the non-linearites you want within your model by analyzing in the time domain instead. However, the solution time may be quite lengthy.

Others hopefully will have better insight.

Good luck,

Steve

 

[meshparts]

Helo Steve,

yes, the modal analysis is linear, but since I'm doing a prestressed modal analysis, the previous statical analysis is nonlinear.

But still, it should be possible to compute complex eigenvalues (damped modal analysis) based on the friction available in the contact zone. Even if the friction is some how linearized.

From the result you can see, that the undamped eigenvalue is bigger than the imaginary part of the complex eigenvalue. So some how ansys computes damping. I'm just wondering, why the tow tipes of listings are so different. And also if the my equation for the coefficient of damping is correct?

Regards
Alexandru Dadalau

 

[seymours2571]

But the friction would not even be linearized.. it would not even be considered in the modal analysis. The prestressed modal analysis only imports the stress/strain distribution from the static analysis to account for any stress stiffening effects.

 

[meshparts]

Are you shure about that??

Take a look at ANSYS help, see Chapter "3.12. Brake Squeal Analysis". It involves friction.

On the other hand, if it true, what you are saying, why do I get a difference between the undamped and damped analysis:

SET TIME/FREQ(Damped) TIME/FREQ(Undamped) LOAD STEP SUBSTEP CUMULATIVE
1 0.0000 7968.5 j 8007.5 1 1 1
0.0000 -7968.5 j

 

[seymours2571]

Frist, sorry about the confusion....I wasn't aware Ansys could even perform this type of advanced modal analysis.

However, after reviewing the help file it appears to me the answers you have make sense. According to the Ansys literature:

"If the real part of the complex frequency is positive, then the system is unstable as the vibrations grow exponentially over time"

Based on that if I am looking at your results correctly you have a positive real value for the undamped anlaysis and a zero real part in the damped analysis. Therefore, what I am seeing is that there is no instability present when you include the damping in the model, but instability becomes present in the undamped condition. I may be way out in left field here, but this is what I am seeing.

Steve