An approximate approach for non-stationary stochastic response of a hysteretic system subjected to combined periodic and stochastic excitation

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Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (16) : 108-116.

KONG Fan1，SHEN Ziheng1，HE Wei2，LI Shujin1

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Abstract

A statistical linearization method is proposed for determining the non-stationary response of a single-degree-of-freedom Bouc-Wen system subjected to a combined stochastic and periodic excitation. Specifically, first, representing the system response into a combination of a deterministic and of a zero-mean random component, the equation of motion is decomposed into a set of two non-linear differential equations, governing deterministic response and stochastic response, respectively. Next, the statistical linearization method is utilized to treat the non-linear stochastic differential equation, deriving the related Lyapunov differential equation in terms of response variance. The system response can be obtained by solving the Lyapunov differential equation and the deterministic equation of motion, simultaneously using standard numerical methods. Finally, pertinent numerical examples demonstrate the applicability and accuracy of the proposed method.
Key words: Bouc-Wen hysteresis model； statistical linearization；nonstationary； combined excitation

Key words

Bouc-Wen hysteresis model / statistical linearization / nonstationary / combined excitation

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KONG Fan1，SHEN Ziheng1，HE Wei2，LI Shujin1. An approximate approach for non-stationary stochastic response of a hysteretic system subjected to combined periodic and stochastic excitation[J]. Journal of Vibration and Shock, 2022, 41(16): 108-116

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