隨機激勵下非線性振動系統(tǒng)特性的定性分析

Characterization of nonlinear vibration systems under random excitation

摘要: 求解李雅普諾夫方程,，可直接獲得平穩(wěn)隨機振動響應協(xié)方差矩陣,。用等效線性化方法處理非線性系統(tǒng)，通過多次迭代求解李雅普諾夫方程可得到穩(wěn)定的等效線性系統(tǒng)參數(shù),，從而獲得一種多自由度非線性系統(tǒng)特性定性分析方法,，為實際的非線性動力學系統(tǒng)建模提供了理論依據(jù)。對幾個實例進行了仿真分析,，結(jié)果驗證了該方法的有效性,。

Abstract: 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.