I'm new to random vibration analysis. Recently I started to try it out in LS-Dyna. I had a small success run with a single part from a tutorial, and my end goal is to able to successful perform the analysis on a large assembly like a commercial airplane. Technically I can run the analysis because I have tutorial, but I hope to gain more of the theory behind it.
A random vibration analysis provides the likely structural response to a spectrum of random excitations. The modal analysis is required since it provides the dynamic characteristics required for the analysis. So, the mode frequencies and shapes are combined in a manner appropriate to the random excitations that you have to give you some form of structural response.
modal analysis is the first step for a linear evaluation of the most important modes (eigenvalues) before a performance analysis. while random analysis is done for the case of nonlinear vibration, spectral analysis is the most helpfull.
Thank you very much for your prompt answers. I have a better understanding of random vibration and modal analysis now. There is another thing that I hope to get answer on. In random vibration analysis, if we have the PSD vs Frequency data, do we still need to perform the modal analysis first? Based on Angus's answer, I get that the modal analysis provides the basis for random excitations, but isn't the PSD vs frequency data be enough to generate the random excitations too? Basically, why do we need PSD vs frequency data when we have modal analysis and vice versa?
The PSD's you are referring to are probably excitation quantities, not response quantities. They are the input forces (or base excitation acceleration levels) that are applied to the system mass and stiffness matrix that result in an output. In order for the transfer function to be generated, though, the dynamic characteristics of the system, ie, the modes and natural frequencies resulting from a modal analysis, need to be calculated. In general finite element codes perform this step without much input from the user, so the user may not be aware that the calculation is taking place. It sounds to me like you really need to take a course in some basic structural dynamic theory before you attempt to do any more dynamic analysis, especially on an aircraft, as a basic understanding is necessary to avoid making some huge blunders.
Thank you for your reply Andrew. I have taken a vibration course that teaches about eigenvalue problems, but you are right that I'm still new to structural dynamics( I didn't know about PSD before). I am reading the Finite Element Procedures by Bathe and other articles to cover all the basics before performing a real analysis. Thanks again for your answer and advice.
In random vibration analysis, the PSD of any response quantity of interest (Sr) is equal to The PSD of input excitation (Se) multiplied in frequency response function (H). The frequency response function of structure can be obtained in two ways. 1) Direct method which is inverse of some matrices and 2) based on modal analysis results. In the direct method, the computer software must obtain the inverse of a matrix whose dimension is very huge. It takes lots of memory and time. using modal analysis results (natural frequencies and mode shapes) one can truncate the mods which do not contribute to the response results. Thus the time of analysis becomes very fast. Another advantage of modal analysis is that it presents results with physical meaning.
1) Random Vibration of the structures by C.Y. Yang ( it is simple and practical)
2) Random Vibration and spectral analysis by Andre Preumont (to me it is perfect)
Dear,
How can we get PSD data to simulate the Random Vibration Analysis?
Thank you!
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