作　　者： ; ;

机构地区： 中山大学

出　　处： 《应用力学学报》 2008年第2期296-298,共3页

摘　　要： 提出了一种改进的等效线性化方法。将现有方法中忽略的高阶谐波项作为等效线性方程的外激励,得到非齐次的等效线性化方程,利用谐波平衡法将该方程分解为一系列常微分方程组,用摄动法求解。算例表明,本文方法不仅提高了等效线性化方法的精度,而且对现有方法不能处理的含偶次非线性系统的分析同样有效。 The equivalent linearization method is widely used in nonlinear dynamics, especially for qualitative analysis. Only the first order harmonic is taken into account for this technique while the higher order harmonics are all neglected. Therefore, the equivalent linearization method works well only for systems with odd nonlinearities, but fails in dealing with systems with even nonlinearities. An improved equivalent linearization method is therefore presented. The neglected terms are treated as external excitations of the equivalent linear system, thus a nonhomogeneous equivalent linear equation is obtained. The harmonic balance method is chosen to solve this equation, then a set of ordinary differential equations (ODEs) with respect to the coefficients of the higher order harmonics of the particular solutions are obtained. The problems under consideration are weakly nonlinear, the perturbation method is used to obtain the approximate solutions of the ODEs. The numerical examples show that the presented method enables to improve the accuracy of equivalent linearization, especially for the systems with even nonlinearities.

关 键 词： 平均法 等效线性化 谐波平衡法

领　　域： [理学] [理学]