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# Equivalency of random vibration and sinusoidal vibrat ion

## Equivalency of random vibration and sinusoidal vibrat ion

(OP)
It is recognized that there is no "real" equivalency between random vibration and sinusoidal vibration. However, are there are any empirical equations based on tests or analysis that provide "approximate" equivalency between random vibration and sinusoidal vibration ?

### RE: Equivalency of random vibration and sinusoidal vibrat ion

You can measure the average RMS of the random signal and then use 1.414 for the value in 0-pk at the dominant frequency.

### RE: Equivalency of random vibration and sinusoidal vibrat ion

Lunney & Crede (see WADC TR-56-503) showed that by assuming Rayleigh distribution of the peak accelerations and combining this with Miner's rule of equivalent damage, the equivalent sinusoidal response acceleration, Aeq is given as

Aeq = Q*Ar

where Ar is the RMS random vibration response acceleration

and Q=[(0.5*(2pi)^.5)^(1/(lambda*alpha))*(lambda*alpha/e)^0.5]

where

lambda = a constant based on experimental data
alpha = slope of the fatigue curve when plotted in log-log coordinates
e = 2.718281828...

Long story short, Q = 2.14-2.17 (usually taken to be 2.14) for most metals.

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