Shaping nonlinear modal manifold of internal resonance system

For system of internal resonance(IR) properties, there will be modal coupling effect while the system linear frequency is commensurable. In order to discuss the dynamic behavior on the IR manifold, we need to include all the coupling manifolds as one invariant manifold, by using the modal invariance property, the system energy can be constrained in this manifold. In this research, an extended normal form method is developed to study the nonlinear Internal Resonance normal mode. The method is based on the traditional normal form method in nonlinear dynamics analysis. 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. The proposed method gives a clear view of the dynamic structures on each modal manifold, which is useful for analyzing some modal coupling phenomenal such as internal resonance (IR) or modal localization problem.