随机激励下自复位结构首次穿越失效研究

First-Passage of Self-Centering System Under Random Excitation

自复位结构遭受地震或强风荷载时,会发生显著的非线性随机振动,这可能导致结构的运行性能大大降低,甚至完全失效.本文旨在研究随机激励下双自由度自复位结构的首次穿越失效问题.应用广义谐波平衡技术,将自复位恢复力进行分解,获得等效随机系统;利用随机平均原理推导出关于幅值的平均Ito随机微分方程;求解后向Kolmogorov(BK)方程得到首次穿越时间的条件可靠性函数和条件概率密度函数通过.作为算例,选用金井清滤波白噪声模型,分析了激励强度D及土层阻尼比ξg取值变化时对条件可靠性函数和条件概率密度函数的影响.通过与Monte Carlo模拟得到的结果进行对比,验证了解析解的有效性.

When the self-centering structure is subjected to earthquake or strong wind load,significant nonlinear random vibration will occur,which may lead to the structural performance greatly reduced or even complete failure.In this paper,the first-passage failure problem of a self-centering structure with two-degrees-of-freedom under random excitation is studied.The generalized harmonic balance technique is used to decompose the self-centering restoring force and obtain the equivalent random system.The average Ito stochastic differential equation with respect to amplitude is derived by means of stochastic average method.The backward Kolmogorov(BK)equation is solved to obtain the conditional reliability function(CRF)and conditional probability density function of the first pass time(PDF).As an example,Kanai-Tajimi filtered white noise model is used to analyze the influence of the change of excitation strength D and soil damping ratioξg on conditional reliability function and conditional probability density function.The validity of the analytical solution is verified by comparing with Monte Carlo simulation results.