An important parameter in random vibration analysis is the peak response, which can be the maximum relative displacement, velocity, acceleration, stress or strain. The peak response can then be compared with the threshold for yielding, ultimate failure, etc. The peak is also important for fatigue analysis, particularly for materials with higher exponents. A common approach is to consider that the peak response is 3σ, where 1σ is the standard deviation. But higher responses often occur > 3σ.
This paper presents a method for estimating the peak response for a desired probability of exceedance. peak_response_random.pdf
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The equation is included in: Vibrationdata Matlab Signal Analysis Package
The function can be accessed via:
vibrationdata > Miscellaneous Function I > SDOF Response: Sine, Random & Miles > SDOF Response: Peak Sigma for Random Base Input > Risk of Overshoot, XRS, URS
This function may also be used for MDOF systems if the positive slope zero-crossing rate is used in place of the natural frequency.
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European Cooperation for Space Standardization, Mechanical Shock Design and Verification Handbook, ECSS-E-HB-32-25A
– Tom Irvine