Spectrum Analysis; Need help to define the PSD frequency table

[vamshi]

Hi,
I am a student working on my thesis regarding Fatigue failure due to Random Vibrations. I have modelled a aluminum beam for the experiment,which is clamped at the center to a shaker. The beam is then excited by a shaker. I did the modal analysis of the beam in Ansys. I have also done the spectrum analysis using ansys. I have been able to excite only 1 frequency which makes the vibration characterisitic more like a sinusoidal or deterministic vibration rather than a random vibration. I do not have any specific criteria to input the values of PSD,Frequency in PSD,Frequency table. I input frequency values closer to the natural frequencies obtained by modal analysis and the PSD values on basis of my shaker limits. So if anyone can guide me in this process, i willl be appreciate their help.
Thanks
Vamshi

 

[LAX]

I assume you have one end of the beam fixed at the shaker and are looking at the response at the free end of the beam. In this case the beam acts like a first order resonant filter to the broadband random input signal. Since a simple beam will have a high Q this will give a predominantly sinusoidal response as you are seeing. The amplitude of response at the resonance frequency is in direct proportion to the Q of the beam. To be able to model or measure the broadband response you must use adequate frequency resolution particularly around the resonance area. Since you will likely be using FFT analysis then the FFT resolution deltaF << BeamFres/2Q.

Also bear in mind in practice that you will see large variations in response depending on the shaker drive levels due to non-linear effects in the beam (larger drive -> lower Q). This may determine a suitable range of forcing function PSDs. Alternatively consider &quot;real life&quot; drive levels that may be experienced in field conditions - say for automotive applications 2g rms may be typical over a 500Hz bandwidth gives 0.008 g^2/Hz.

 

[dampit]

First, do a sine sweep and find the resonant frequencies. 1st Bending mode will be about 6.3 times lower than 2nd bending mode, 3rd will be 17x higher than 1st-B.
In a cantilever beam, the response near the tip will be mostly mode 1, but near the root you should see other modes or near the mid-span you should see mode 2 better.

Then, open up the bandwidth on the random input to cover these first three modes, or excite from 10-2000 Hz. Use an input level of about 10 grms Overall or PSD=0.05 G^2/Hz. This will give you Broad Band Random Response. If your input spectrum doesn't cover the higher modes, then you won't excite them.

Note: if you only excite a bandwidth centered on the frist mode, then you'll get what is called Narrow Band Random response,and depending on your noise generator you should get +/- 2.8 standard deviations in random amplitude. Beyond +/-4 stdev, the random fatigue properties of metals don't change. Exciting higher order modes (Broad Band Random Response), have a small impact on random fatigue characteristics.

I suggest you read some papers by Ronald Lambert, who did most of the fundamental development research in Random Vibration Fatigue.