## random vibration analysis

## random vibration analysis

(OP)

I am looking for empirical/handy formulae or equations that can be used to calculate the resulting displacement and forces of simple strucures (plates, beams, etc.) that are subjected to random vibration. The input random vibration load is presented in the form of power-spectral density (G**2/Hz) versus frequency(hz). Amplification factor/transmissibility factor need to be considered.

## RE: random vibration analysis

This information comes from Chapter 13, Random Vibrations, of "Theory of Vibration with Applications", 3rd Ed., by Thomson.

Define S(f) as the power spectral density function

Define H(f) as the frequency response function for the structure. Each degree of freedom will have its own H(f), and it can be determined by shaker testing at varying frequncies.

Next, pick several discrete frequencies, equally spaced over the spectrum range. Calculate the mean square response at each frequency. It is defined as

a^2 = S(f)*¦H(f)¦^2*df, where df is the frequency increment. Sum up all of the a^2 values, and take the square root. This will give the acceleration response of the structure. For a multiple degree of freedom system, each DOF will have its own results.

It is possible to calculate the probability that a given excitation will be exceeded. See Thomson for details.

## RE: random vibration analysis

## RE: random vibration analysis

http://www.vibrationdata.com/tutorials.htm

Specifically, refer to the vibration response spectrum tutorial, vrs.pdf. Also, refer to psdinteg.pdf.

Please let me know if you have any questions after reading these tutorials.

Sincerely, Tom Irvine

Email: tomirvine@aol.com

## RE: random vibration analysis

## RE: random vibration analysis

Have you already have anything on the subject?

## RE: random vibration analysis

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## RE: random vibration analysis

RMS Response = sqrt(pi/2 * fn/zeta * PSD), Schiff D. - "Dynamic Analysis and Failure Modes of Simple Structures"

## RE: random vibration analysis

i c that ur working on random vibration analysis of beams...

how do u apply the random loads on the beam...i am using MSC/NSATRAN v70.7 should i use a large mass ..and what should be th order of the mass..

do we get the out put as PSD ,Mean and mean square response for the load applied ....what other data is equired to specified for th analysis

please help me

gautam

## RE: random vibration analysis

"

I have posted some downloadable tutorials on random vibration at:..."By the way... there is

A SMALL FEE!I have found your advice on the forum to be very helpful, and I'm sure I speak for all in saying that you are a valued contributor. But in the future it might be helpful if you could warn us of the fee so that the 99% of us who don't routinely pay for information on the internet will not waste time following your links.

## RE: random vibration analysis

You do not say if your random loading is distributed or applied at a point. I would be tempted to use an FE model if it is the former.

Regards

Michael

## RE: random vibration analysis

then you can use classical modal analysis in conjunction

with random vibration analysis. The response power spectra

can be related to the input excitation cross-spectra by

way of the system spatial modes and transfer function.

Check out a paper by Dowell(1995) on Asymptotic Modal

Analysis for some details...the paper will give most

of the important relations and will give an easily calculated result in the asymptotic limit.