A plain approach for center manifold reduction of nonlinear systems with external periodic excitations

Abstract

We present a relatively plain, direct and intuitive methodology that accomplishes model order reduction on the invariant center manifold of large-dimensional nonlinear systems subjected to external periodic excitations. This methodology is applicable to parametrically excited (periodic coefficients) and constant coefficient nonlinear systems. Our approach is empowered by intuitive augmentation of system states and is further liberated from typical special strategies such as the need for a ‘book-keeping’ parameter, a detuning parameter and minimal excitation. Consequently, it is relatively straightforward to implement and applicable to a broad range of nonlinear systems with external periodic excitations. Two illustrative application cases are investigated, and their subsequent results validate the accuracy of our approach. The first case considers a parametrically excited system with a single external periodic frequency excitation. A mass-spring-damper system with constant coefficients and two heterogeneous external frequency excitations is considered in the second example. In both cases, the long-term steady-state behavior analysis shows exact or cogent agreement between the original and the reduced-order system.