平稳随机激励下耦合Newmark滑移系统的可靠性分析

基于随机激励的离散形式,对耦合Newmark系统的动力可靠度问题进行解析分析。平稳随机激励下,耦合Newmark系统初始滑移极限状态方程可以写成n个标准正态随机变量的显式线性函数,并能给出可靠度指标的理论解。对于以相对滑移量为临界状态的情况,极限状态方程是n个标准正态随机变量的隐式函数,可借助静力可靠度方法进行求解。算例表明,系统初始滑移的设计点激励是以潜在滑动体自振频率为主频,振幅渐增的谐振时程;后者的失效概率与摩擦系数成非线性关系,存在合适的摩擦系数使失效概率最小。

Dynamic reliability analysis of the coupled Newmark sliding system under stationary random excitation

Based on a discrete representation of the input random process,the dynamic reliability of a coupled Newmark sliding system under stationary excitation is investigated analytically.When the initial sliding of the system induced by stationary excitation is considered,the limit-state function can be expressed as an explicit linear function of n standard normal random variables,and the theoretical solution of reliability index can be obtained.If sliding more than a certain amount of relative displacement is considered as the failure criterion of the system,the limit-state function is expressed as an explicit nonlinear function of n standard normal random variables,and an approximate solution can be gained by using the static reliability methods.Examples show the design point excitation resulting in the initial relative sliding of the system is a harmonic wave with increasing amplitude,and its frequency is equal to the one of the system.There are nonlinear relations between probability values of failure for the system sliding more than a certain displacement and coefficients of friction of the system,and the optimal coefficient of friction which makes the minimum probability of failure can be found.