随机激励下非线性振动系统特性的定性分析

求解李雅普诺夫方程,可直接获得平稳随机振动响应协方差矩阵。用等效线性化方法处理非线性系统,通过多次迭代求解李雅普诺夫方程可得到稳定的等效线性系统参数,从而获得一种多自由度非线性系统特性定性分析方法,为实际的非线性动力学系统建模提供了理论依据。对几个实例进行了仿真分析,结果验证了该方法的有效性。

Characterization of nonlinear vibration systems under random excitation

From the solution of the Lyapunov equation, the stationary random vibration response covariance of a structure can be directly obtained. The nonlinear system is linearized by the equivalent linearization method, and the Lyapunov equation is solved by iterations and the stationary equivalent linear parameter of the nonlinear system is obtained. This is a characterization method for the nonlinear vibration system of multiple degrees of freedom (DOFs). The proposed method provides a theoretical basis to choose the model of the nonlinear dynamic system. A simulation is carried out to analyze an examples of the nonlinear system, and the results show that this method is valid.