A Method of Nonlinear Modal Superposition for Weakly Nonlinear Autonomous Systems

Abstract

For a weakly nonlinear autonomous systems, the nonlinear coordinate transformation is provided in the form of power series expansions and the mathematical transformation from the physics system coordinate to the modal coordinate is presented. And then, according to the relations between physics system coordinate and modal coordinate, a method of nonlinear modal superposition is obtained. Using this method, the general solution of the vibration under any initial condition can be answered. In order to explain the applications of the method, numerical examples are presented in this paper.