色噪声与确定性谐波联合激励下Bouc-Wen动力系统响应的统计线性化方法

Stochastic response of a hysteresis system subjected to combined periodic and colored noise excitation via the statistical linearization method

提出了一种用于求解色噪声和确定性谐波联合作用下单自由度Bouc-Wen系统响应的统计线性化方法。基于系统响应可分解为确定性谐波和零均值随机分量之和的假定,将原滞回运动方程等效地化为两组耦合的且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。利用谐波平衡法求解确定性运动方程,利用统计线性化方法求解色噪声激励下的随机运动方程。由此,可导出关于确定性谐波响应分量Fourier级数和随机响应分量二阶矩的非线性代数方程组。利用牛顿迭代法对上述耦合的代数方程组进行求解。数值算例验证了此方法的适用性和精度。

A statistical linearization method is proposed for determining the response of a single-degree-of-freedom Bouc-Wen system subjected to combined colored noise and harmonic loads.The proposed method is based on the assumption that the system response can be decomposed into the sum of deterministic harmonic and zero-mean random components.Specifically,the equation of motion is decomposed into two sets of nonlinear differential equations governing deterministic response and stochastic response,respectively.The harmonic balance method is used to solve the equation of motion with deterministic excitation,whereas the statistical linearization method is utilized to obtain the variance of the stochastic response.These treatments lead to a set of coupled algebraic equations in terms of the Fourier coefficients of the deterministic response and the stochastic response variance.Standard numerical schemes such as Newton’s iteration method are adopted to solve the preceding non-linear algebraic equations.Pertinent numerical examples demonstrate the applicability and accuracy of the proposed method.