A Method of Normal Mode Invariant Manifolds for Hopf Bifurcation Solutions of a Class of High Dimensional Systems

Based on the theory of nonlinear normal modes and normal form, a method of normal mode invariant manifolds for the analysis of simple Hopf bifurcation solutions is presented. It aims at a class of nonlinear structural vibrating systems and mechanical-electrical coupled systems. The method does not require diagonalization and finding the central manifold. It is only necessary to construct the center normal mode manifold by solving the coefficients of nonlinear normal modes. Compared with the results of other general methods, it is shown that the method is correct and effective.