Analysis of Nonlinear Normal Modes by Extended Normal Form Method

An extended normal form method is developed here to study the nonlinear normal mode. The method is based on the traditional normal form method in nonlinear dynamics analysis. It will be shown that the concept of linear modal space can be extended to nonlinear modal space and the linear modal space is tangent to the nonlinear modal space. Therefore, the purpose of this paper is to provide a framework of nonlinear coordinate transformation that can transform a nonlinear system into nonlinear modal coordinate. By using the modal invariance property, we will form a set of homological equations; and the coordinate transformation process is converted to a coefficients-to-be-determined problem. Compared with the traditional normal form method, the extended normal form method bares the merits of intuitive, ease of use and gives more quantities description of system behavior, and the transformed modal equations can be used to study the modal behavior of specific normal mode