An Efficient Analysis of High-Order Dynamical System with Local Nonlinearity

Abstract

This paper deals with dynamical systems including spatially localized nonlinear substructures. In these cases, the differential equations of motion consist of the coupled linear and nonlinear subsets. According to the feature of such systems, a modal transformation is used, by means which the number of degrees of freedom of the linear subset is reduced significantly and the localized feature of the nonlinear subset still remains. In accordance with this reduced model, a modified Newmark method that is unconditionally stable is proposed to integrate the responses of the reduced system. The advantage of this method is that the nonlinear iterations only need to be executed on localized nonlinear parts of the system equations. The numerical schemes of this study are applied to a large-order flexible rotor with two elliptical bearing supports. The periodic solutions and long term behaviors of the system are investigated numerically, which reveals many interesting phenomena.