How can I determine amplification factor

[winpop123]

Sorry but amplification factor may not be the correct term but bear with me....

I have the following:
1. A hollow aluminum tube with a mass on the end. I can calculate the anticipated natural frequency with a hand calculation.
2. I have a PSD curve out of MIL-STD-810 that the structure will need to survive
3. I do not have the luxury of a full blown dynamic analysis tool for calculating mode shapes etc.
4. I do have static FEA capability

What I would like to do is determine natural frequency of the tube and then determine what "amplification factor" the structure will see at the prescribed input at the frequency of interest.

I would then use that acceleration input into my FEA to calculate a resultant stress. With that value I would apply 3 sigma, Miners equation, comparison to S/N curves etc to make a determination on the life of the structure.

Can I get there from here?

Thanks

 

[tomirvine]

You can analyze this problem as a hand calculation.

1. Calculate the natural frequency.
2. Model the system as a single-degree-of-freedom system.
3. Assume one or more damping values, such as 5% or 1%.
4. Uses Miles equation to calculate the response of the system to the base input PSD for each damping value.
5. Calculate the resulting bending moments and shear forces, particularly at the boundaries.
6. Calculate the resulting stress levels.
7. Find the S-N curve for the material.
8. Use Miner's cumulative fatigue formula.
9. Also give some consideration to stress concentration factors, stress corrosion, etc.

Steinberg's Vibration Analysis for Electronic Equipment has some very good examples for this calculation.

I have also posted some papers on fatigue at:

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

Tom Irvine

 

[winpop123]

Thanks - I don't do this on a regular basis. I was stuck at the Miles equation. I found it in my files and was able to calculate the resultant Grms in x,y, and z.

Thanks

 

[GregLocock]

Incidentally, FEA would have been no real help - the big unknown is the damping factor.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.