提出了一种用于求解非平稳随机和确定性谐波联合作用下，单自由度滞回系统非平稳响应的统计线性化方法。首先，在系统响应表示为确定性和零均值非平稳随机分量之和的基础上，将原滞回运动方程等效地化为两组耦合的、分别以确定性和随机动力响应为未知量的非线性微分方程。随后，利用统计线性化方法处理非平稳激励下的随机运动微分方程，导出关于随机响应分量二阶矩的Lyapunov微分方程。联立Lyapunov微分方程与确定性运动微分方程，并利用标准数值算法求解响应。最后，数值算例验证该方法的适用性和精度。
关键词：Bouc-Wen滞回模型；统计线性化；非平稳；周期和随机联合激励
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
关键词
Bouc-Wen滞回模型 /
统计线性化 /
非平稳 /
周期和随机联合激励
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Key words
Bouc-Wen hysteresis model /
statistical linearization /
nonstationary /
combined excitation
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