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Stochastic dynamic response analysis of hysteretic nonlinear systems based on state-space-split method[J].计算力学学报,2021,38(1):1~7

Stochastic dynamic response analysis of hysteretic nonlinear systems based on state-space-split method
Stochastic dynamic response analysis of hysteretic nonlinear systems based on state-space-split method

DOI：10.7511/jslx20200311001

 作者 单位 徐严钢 天津大学 建筑工程学院, 天津 300072 朱海涛 天津大学 建筑工程学院, 天津 300072天津大学 滨海土木工程结构与安全教育部重点实验室, 天津 300072 柳国环 天津大学 建筑工程学院, 天津 300072 刘治国 天津大学 建筑工程学院, 天津 300072天津大学 滨海土木工程结构与安全教育部重点实验室, 天津 300072中国市政工程华北设计研究总院有限公司, 天津 300074

采用SSS （state-space-split）法，建立了引入Bouc-Wen滞回模型的杜芬非线性系统在高斯白噪声激励下的概率密度函数（PDF）的近似求解方法，分析了其随机动力响应变化规律。首先，将Bouc-Wen滞回模型引入杜芬非线性系统，分别考虑非线性系统中的几何非线性和材料非线性对动力响应的影响。随后，对该模型进行了等效线性化（EQL）处理，基于等效线性化法结果，介绍了SSS法的简化方法和计算原理，并通过该方法求解了三维FPK方程的近似联合概率密度函数。最后，将该方法应用于三个案例和一个工程实例，通过求解其概率密度函数分布及动力可靠度验证了提出方法的适用性、可行性和优越性。

Using the state-space-split (SSS) method,this paper develops an approximate solution procedure for the probability density function (PDF) of a Duffing nonlinear system with the Bouc-Wen hysteretic model under Gaussian white noise excitation.First,the Bouc-Wen hysteretic model is introduced into the Duffing nonlinear system.This model considers the effects of geometric nonlinearity and material nonlinearity on the dynamic response of the nonlinear system,respectively.Subsequently,the equivalent linearization method (EQL) is used to analyze this nonlinear system.Based on the results of EQL,the simplification approach and computation principle of the SSS method are introduced and it is adopted to solve the approximate joint PDF of the three-dimensional FPK equation.Finally,the proposed method is applied to three cases and an engineering example.Its applicability,feasibility and superiority are verified by analyzing the PDF distribution and the dynamical reliability of the nonlinear system.