Ys. Zhou et al., A MODEL FOR GENERAL PERIODIC EXCITATION WITH RANDOM DISTURBANCE AND ITS APPLICATION, Journal of sound and vibration, 203(4), 1997, pp. 607-620
Many vibration problems involve a general periodic excitation such as
those of a triangular or rectangular waveform. In practice, the period
ic excitation may become disordered due to uncertainties. This paper p
resents a stochastic model for general periodic excitations with rando
m disturbance, which is constructed by introducing random amplitude an
d phase disturbances to individual terms in the Fourier series of the
corresponding deterministic periodic function. Mean square convergence
of the random Fourier series are discussed. Monte Carlo simulation of
disordered sawtooth, triangular, and quadratic wave forms are illustr
ated. An application of the excitation is demonstrated by vibration an
alysis of a single-degree-of-freedom (SDOF) hydraulic valve system sub
jected to a disordered periodic fluid pressure. In the present study o
nly the phase disturbance is considered. Effects of the intensity of p
hase modulation on up to fourth order moment response and the converge
nce rate of the random Fourier series are studied by numerical results
. It is found that a small random disturbance in a general periodic ex
citation may significantly change the response moment. (C) 1997 Academ
ic Press Limited.