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# Interface force recovery from Random Vibration using FEA

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## Interface force recovery from Random Vibration using FEA

(OP)
Typically we use quasi-static loads on our system level structures. Because the system level models are so large we often recover interface forces from the system model (of different mating components) and then apply these forces at bolted joints of detailed stand alone 'fitting' models. Then we recover stresses in the joints. In this particular instance we have a random vibe load for our system model. We are using cbush elements to recover the forces and as you all know the RMS force values have no phase information and thus are all 'positive' in nature. I realize the correct manner to do the proper stress analysis would be to incorporate the detailed fitting model into the system model and recover RMS stresses. Does anyone have any experience applying random vibe interface forces to stand alone highly detailed fitting models? Applying all 'positive' values isn't really appropriate.

### RE: Interface force recovery from Random Vibration using FEA

Hmmmm. That's a three pipe problem, as Holmes'would put it. I think the answer is that you can't safely do much without phase information, but our excellent friend at http://www.vibrationdata.com may well have appropriate advice. The fundamental issue is thst if you just add every frequency component in phase you will deliver a most unlikely shock.

Cheers

Greg Locock

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### RE: Interface force recovery from Random Vibration using FEA

Don't confuse the RMS magnitudes of the forces whether individually or summed, with the time evolution of the actual forces. If you do the phase information is lost. In otherwords, all modes word be excited in phase and produce grossly misleading results.

Basic maths...

### RE: Interface force recovery from Random Vibration using FEA

(OP)
Thanks GregLocock and hacksaw for the replies.
I'll check out the vibrationdata site.

### RE: Interface force recovery from Random Vibration using FEA

what if you work at the FRF levels?

• for each cbush in your joint extract the FRF (based on 1g sine sweep analysis). Each FRF is complex
• at each frequency you can add all the Re and Im part of the all the FRFs
• once you have the SUM FRF at each freq. f, estimate the magnitude: SQRT(Re^2+Im^2)
• if you then take at each freq. f: PSDinterfarce(f)= mag^2*PDS(f),you might end up with the PSD "resultant" for the interface
Just a thought and might be totally wrong !!

### RE: Interface force recovery from Random Vibration using FEA

(OP)
Thanks JXB0809,
I'll look into that. Thanks for your thoughts.

### RE: Interface force recovery from Random Vibration using FEA

Feel free to report your thinking

### RE: Interface force recovery from Random Vibration using FEA

Here's a different perspective that I've not verified:
1. Create 'long' time domain signal that satisfies the RMS profile
2. From FEA, extract individual transfer functions of force_at_bolts/input_motion (complex numbers)
3. Apply transfer functions on input signal to calculate forces in time domain

The output will have phase content. Interactions of closely spaced modes could be accounted for. Statistical analysis needs to be performed on the input and output to verify the law of large numbers is satisfied.

In principle, evaluations can be done in the time domain peak loads.

Kind regards,
Jason

### RE: Interface force recovery from Random Vibration using FEA

with such approach don't you need a signal of very long duration to satisfies the random assumption. Might be very prohibitive to do an analysis with such signal!

### RE: Interface force recovery from Random Vibration using FEA

That's a good question! I re-framed the question as: "how many normally distributed random points are needed before the standard deviation converges?"

A simple Matlab code below plots the standard deviation of different data block size. At around 10^5, it appears to converge.

#### CODE --> matlab

pow = 1:0.5:8;
tries = 10;
s=zeros(length(pow), tries);
for ct2=1:tries
for ct = 1:length(pow);
N = round(10^pow(ct));
q = randn(N,1);
s(ct,ct2) = std(q);
end
end
figure(1)
loglog(10.^pow, s, '*-')
xlabel('Length of Random Values'); ylabel('Standard Deviation');
title('Standard Deviation of Various Length of Gaussian Random Numbers')
grid on 

Kind regards,
Jason

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