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Journal of Vibration and Control
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A Closure Procedure for Random Vibration Parametric Resonances

R. V. Bobryk

Institute of Mathematics, Swietokrzyska Academy, 25-406 Kielce, Poland and Institute APMM, Ukrainian Academy of Sciences, 79-060 Lviv, Ukraine, bobryk{at}pu.kielce.pl

A. Chrzeszczyk

Institute of Mathematics, Swietokrzyska Academy, 25-406 Kielce, Poland

L. Stettner

Institute of Mathematics, Polish Academy of Sciences, 00-950 Warszawa, Poland

We investigate the mean-square stability for single-degree-of-freedom linear systems with random parametric excitation. The excitation is assumed to be of the form of a Gaussian stationary non-white process. We propose a new numerical approach to determine regions of parametric resonances based on a closure procedure for hierarchy of moment equations. Mean-square stability charts are obtained using the numerical analysis of eigenvalues for large-scale matrices. The results show three parametric resonances for narrow-band excitations.

Key Words: Random vibration • parametric resonance • stability chart • non-white noise excitation

Journal of Vibration and Control, Vol. 11, No. 2, 215-223 (2005)
DOI: 10.1177/1077546305049052
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