Page 443 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

430 Random Vibrations Chap. 13

Sine wave Wide-band record Narrow-band record

PM

The variance associated with the Rayleigh distribution is

o-A = A ^ ~ { A f =
2
:.(T^ - 30- (13.4-13)

Also, the probability of A exceeding a specified value A ct is

Prob[^ >Ao-]= (13.4-14)

which has the following numerical values:

A P [ A > A ct]
0 100%
1 60.7%
2 13.5%
3 1.2%

Three important examples of time records frequently encountered in practice
are shown in Fig. 13.4-7, where the mean value is arbitrarily chosen to be zero. The
cumulative probability distribution for the sine wave is easily shown to be

P{x) = 4 + :^ sin '