非线性振动的模态方法

The Modal Method of Nonlinear Vibrations

自从60年代Rosenberg 提出非线性振动系统模态概念以来,国外许多学者对之进行了大量的研究,取得了不少成果。但迄今为止,只研究了保守系统的模态,利用模态进行研究的也仅仅是系统的周期响应。我们将现有的非线性系统模态的概念加以发展,较系统地提出了一种利用非线性系统的模态研究非线性振动问题的方法——非线性振动的模态方法。该方法不仅适用于保守系统,而且适用于非保守自治系统和非自治系统;既可用来研究系统的周期响应,也可用来研究系统的非周期响应。

Since Rosenberg developed the concept of normal modes of nonlinear vibration systems in 1960s,much research has been carried out and many important results have been obtained.But,so far only the normal modes of conservative systems have been dealt with,and only periodic responses of the systems have been studied by means of normal modes.Recently,the concept of normal modes of nonlinear systems has been further developed by the authors of this paper,and a modal method of nonlinear vidrations has been systematically presented.The method is applicable not only to conservative systems,but also to autonomous and nonautonomous systems, and can be used to study both periodic and nonperiodic responses of the systems.