aliasing after non-linear FEA 1

[KalleH]

I am performing a transient FEA on a non-linear system. The loading signal has been filtered properly and has no aliasing.

However, as the system is non linear, the output signal will have a wider frequency content. How do I know if aliasing has occurred or not?

I assume that the key somehow is that the frequencies of the higher freequency modes together with their participation factors act as a filter. However, if this is true - how do I determine this?

Chers!

 

[tomirvine]

As a rule-of-thumb, the sample rate should be at least ten times higher than the maximum analysis frequency for time domain analyses.

You can evaluate the significance of each mode based on the participation factor and the effective modal mass. You can then specify the number of modes to be included in the transient analysis.

You effectively lowpass filter the response by limiting the number of modes.

If necessary, you could interpolate your loading function.

Tom Irvine

http://www.vibrationdata.com

 

[KalleH]

Tom,

I guess the approach you describe is the way to go for a linear system, where I can use mode superposition. However, in this case I have non-linear springs, and hence the modes at lower amplitude will not give me all the information I need for the analysis.

Hence I solve the problem in Ansys as a Full and not Mode Superposition analysis and can therefore not limit the number of modes used.

Let me therefore rephrase my question: Is there any way to limit or determine the upper limit of the frequency content for a full analysis of a non-linear system.

Thanks!

 

[GregLocock]

No.

take the simplest non linear event - a step function.

Its Fourier series is infinite.

So you have to apply engineering judgement, look at the spectra of the results and just accept that you have stopped getting meaningful data when it is down to (say) 80 dB of the low frequency content.

And as I was recently told, what's the point of modelling something you can't verify? Use the same frequency/amplitude cut offs as your experimental data used.





Cheers

Greg Locock

 

[MikeyP]

KalleH,

I kind of see what you are thinking. However, ailiasing is a consequence of sampling ie a tranformation from the continuous time real world to the discrete time world inside your signal analyser/computer. The time-stepping integration solver in your FE code is already working in the discrete time world (hence the phrase "time-stepping"). But yes, you will lose information about the non-linear response at high frequencies unless you have an infinitely small time step on your analysis

Your comments about higher frequency modes and participation factors are not relevant. The non-linear FE solver knows nothing of the modal behaviour. It acts on the physical coordinate mass and stiffness matrices.

You don't say what form your non-linear springs take, but I'm guessing it is going to take the form of some sort of polynomial, freeplay or bi/tri-linear characteristic. These sorts of non-linearities give you responses at the harmonics (or possible sub-harmonics) of the excitation frequencies. But the level of response decreases rapidly with increasing harmonic order. As well as the limit of verifiability (is that a word?) mentioned by Greg due to the maximum measurement dynamic range, there is also the limit of machine precision (the numerical dynamic range in your computer, probably double precision in your FE code) and the accuracy and precision of the integration algorithm used by your FE solver. The default accuracy of your FE solver is probably set quite low so that the solution runs at a reasonable speed.

I have done some work using different integrators and the differences between using say the Adams-Bashforth multi-step integration used by many FE solvers and the 5th order Runge-Kutta single step integrators used by our in-house software for even quite simple non-linear problems are very noticable.

My rule of thumb for non-linear behaviour is to use a sampling rate (experiment) or time-stepping interval (FE) which gives a resolution of 32 points per cycle at the maximum frequency of the input signal. This will give a resonable degree of accuracy as high as the 5th harmonic and will even contain some 7th harmonic information.

M

--
Dr Michael F Platten