Postprint version. Published in Journal of Sound and Vibration, Volume 203, Issue 4, June 19, 1997, pages 607-620. The definitive version can be found online at http://dx.doi.org/10.1006/jsvi.1996.0869
At the time of publication, the author Mohammad N.Noori was affiliated with Worcester Polytechnic Institute. Currently, July 2008, he is the Dean of the College of Engineering at California Polytechnic State University - San Luis Obispo.
Many vibration problems involve a general periodic excitation such as those of a triangular or rectangular waveform. In practice, the periodic excitation may become disordered due to uncertainties. This paper presents a stochastic model for general periodic excitations with random disturbances which is constructed by introducing random amplitude and 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 illustrated. An application of the excitation is demonstrated by vibration analysis of a single-degree-of-freedom (SDOF) hydraulic valve system subjected to a disordered periodic fluid pressure. In the present study only the phase disturbance is considered. Effects of the intensity of phase modulation on up to fourth order moment response and the convergence rate of the random Fourier series are studied by numerical results. It is found that a small random disturbance in a general periodic excitation may significantly change the response moment.