Numerical studies of dynamic stability under small random parametric excitations

Roman V. Bobryk; Andrzej Chrzeszczyk

Roman V. Bobryk Institute of Mathematics, Jan Kochanowski University, Kielce
Andrzej Chrzeszczyk Institute of Mathematics, Jan Kochanowski University, Kielce

Abstract

An efficient numerical procedure is proposed to obtain mean-square stability regions for both single-degree-of-freedom and two-degree-of-freedom linear systems under parametric bounded noise excitation. This procedure reduces the stability problem to a matrix eigenvalue problem. Using this approach, ranges of applicability to the well-known stochastic averaging method are discussed. Numerical results show that the small parameter size in the stochastic averaging method can have a significant effect on the stability regions. The influence of noise on the shape of simple and combination parametric resonances is studied.

Keywords

random vibration, stochastic averaging, mean square stability, bounded noise,

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