Random Response Analysis

Nathan_22110

Hello everyone,

 

I have been following the OS-T 1325 Random Response Analysis OptiStruct tutorial last times, and I have a few questions about it:

 

- Firstly, eventhough I have clearly understood what Frequency Response and Transient Dynamic Analysis do, I don't see the point of the Random Response.

• Frequency Response Analysis gives the mechanical steady-state response y (such as displacement, stress, etc) for oscillatory excitation x(f) with a frequency f between a range [f1,f2]
• Transient Dynamic Analysis gives the mechanical response y(t) for time-dependent loads x(t). So we get mechanical values (stress, strain, etc) throughout the time history.

I understood that it is based on a Frequency Response Analysis with a PSD (which is kind of a Fourier transform) so a frequency information, and I understood that is useful when the load is said as 'random' that is to say we cannot predict the shape, values, mean such as wind on an aircraft, imperfect road surface on a car, etc. In any case, we need data as input so what do we use?

 

As an example, let's say we focus on a car moving on a road with imperfect surface and we record acceleration of a part throughout time. Why do we use Random Response Analysis in such a case? Is it because we cannot be sure that the signal is perfectly representative of the duty cycle of the car so it is unsuitable to run a Transient analysis? Thus, we run a Random Response Analysis which is more 'statistical' and will give mechanical responses that are likely to occur for a random signal with frequency in the range of the input? But if that is right, why the input is suddenly likely representative of the duty cycle? By the way, why do we use a PSD as an input?

I read this article https://blog.altair.com/random-response-fatigue-analysis/    and many other pages but even with that I'm still not convinced of what is the prupose of Random Response Analysis and how it orks. Concerning the results of such analysis, what does the RMS stress represent? Should we compare it to the yield strength? Or is it the stress you directly refer to in an S-N curve to assess the number of cycles before the structure fails, or do you set-up a fatigue analysis from it?

Finally, it is remains after all a Frequency Response Analysis so how does it use the PSD input? Does it multiply the Frequency response analysis ouput with the 'power' y-values of the PSD?

 

-Secondly, I don't understand in the RANDPS load collector what are the J and K input. It is said in the User Guide that there is a excited load and an applied load? How can they be different, what does that mean?

-Thirdly, what is the difference between the PSD(t) stress and the RMS stress?

 

 

Thank you for your help.

Nathan

 

 

 

Nathan_22110

Hi,

 

I come today because I think I have made progress in understanding some points of Random Response Analysis and it could be helpful to have your validation. 

 

- For my first questions, they are still valid. I still do not understand these points ; except that the 1-sigma value RMS stress (and 2sigma is 2* 1sigma etc) is the maximum stress that is likely to occur at a point of interest throughout the frequency range. So you have 32% chance to be above that 1-sigma limit. 

 

- Then, for the second question, I think that I have understood that if J and K input are different, you have to give as input the cross power spectral density of two  sources that is an information about the power shared by a given frequency for the two signals. But I still do not understand what 'excited' load and 'applied' load mean for a Dynamic mechanical system?

-For the third question, I have understood that the RMS stress is the average on the whole frequency range, RMS cumulated is only the average on a part of the frequency range, and the PSD stress is the stress due to excitation to the current chosen frequency?

 

Thank you for you help,

Nathan

 

Rex_22369

To one of your question, why use frequency domain instead of time domain:

 

Traditionally fatigue analyses have been dealt with by defining the time variation of the loading. Sometimes these time histories become very complex, long, and even random in nature, making conventional transient FE analysis and even pseudo-static fatigue analyses very time consuming, cumbersome, and inconvenient.
Dynamicists have long used frequency domain techniques to understand responses to structures subject to these types of loading, mainly out of necessity to speed up computation times and reduce disk storage needs, but also to understand dynamic behavior.

I was trying to give you a good answer, but I think it's better to find something from the famous book or article, the above answer is from Embedded Vibration Fatigue User’s Guide of Nastran, this is only part of the answer, in this document, you can find almost all your answer, they also compared the stress and damage by using time domain and frequency domain in random fatigue simulation.

Hope it helps you! 

Meanwhile, I hope this forum can answer the difficult questions too....