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Vibration fatigue - There are several methods. The simple approach is to generate SN data under Narrow band random condition - i.e generate a Srms vs. Cycle curve. Simply, predict a PSD using a analysis method, calculate the RMS and look up cycle to failure on your RMS Stress vs. cycles to...

In the aerospace world, we would run a qual-test 600 sec per axis. This usually is adequate unless the failure mode can't be excited in a single axis. Most large shaker tables can be turned over on their sides to excite the x or y direction as well as vertical z-dir. But, there are such things...

For Sinusodal motion ONLY G = Acceleration in g-units D=inches peak to peak (Double-Amplitude) F=Frequency in Hz G=0.0511 F^2 D Note: Convert this to Grms by Grms = 0.7071 G Grms=(0.0511 / 0.7071) F^2 D = 0.072 F^2 D Converserly, d0 = Peak Displacement = 9.8 G / F^2 (Zero to Peak...

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

A must for structural engineers is Blevins: Formulas for Natural Frequencies and Mode Shapes, Roarks-Formalus for Stress and Strain, Thomson - Theory of Vibration, Crandalls - Random Vibration, Bendat and Piersol - Random Data, and of course The Shock and Vibration Handbook.

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...