CLASSIFICATION OF NONLINEAR NORMAL MODES AND THEIR NEW CONSTRUCTIVE METHOD
非线性模态的分类和新的求解方法

The definition of the nonlinear normal modes is given by introducing the undivided even dimensional invariant manifold, and a new kind of normal modes (i.e. coupled nonlinear mode) are proposed which may classify all the normal modes expected in physical systems. This idea of classification may form a new base of constructing the nonlinear normal mode theory. Modal oscillators obtained by the method presented here are of Normal Form type,which are simplest in expression and can represent the main dynamical behavior of the original systems. From which the information, such as nonlinear frequency and nonlinear stability etc., can be easily gained. The method is suitable to analyse the general multi degree freedom systems and odd dimensional nonlinear dynamical systems; it can be used to construct not only uncoupled normal modes but also coupled normal modes of the systems with internal resonance. The solutions of the above problems have not been found in the literatures up till now.