二自由度滞回系统对平稳随机激励的复模态分析方法

Complex Mode Analysis Method for Two DOF System With Hysteresis to Stationary Random Excitation

提出了一种求二自由度滞回系统对平稳随机激励的响应的方法．具有非线性滞回特性的二自由度系统，其振动方程中的非线性项不仅与位移及速度有关，还随着加载和卸载而有不同的函数形式．为了求这种系统的响应，本文采用复模态方法及统计线性化方法，详细讨论了加载与卸载对应的积分区间的划分，通过积分求出了等效线性化系数，并将实数域上的有关方法推广到复数域上，导出了系统在物理坐标下的均方根响应．作为算例，计算了二自由度双线性滞回系统对平稳基础激励的位移，加速度均方根响应，并将所得结果与数值模拟结果进行了比较，二者吻合很好．

A method for finding the responses of two DOF systems with hysteresis to stationary random excitation is given.The.nonlinear terms in the vibration equations of such systems not only have relation to displacement and velocity,but also have different function forms depending on their loading and unloading process.To solve this problem,the complex mode method and statistical linearization method are employed,the dividing of integrvtion intercals corresponding to the loading and unloading process are discussed in details in arder to obtain the equivalent linearization coefficients through integration,and some methods used in real number domain are generalylied to complex number domain.And then the root mean square responses of the system under physical coordinate are derived.As an example,a two DOF system with bilinear hysteresis is considered,and its results are compared with those obtained by Monte Carlo simulation method.