An efficient analysis of high-order dynamical system with local nonlinearity

This paper deals with dynamical systems including spatially localized nonli near substructures. fn these cases the differential equations of motion con sist 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. la accordance wit h this reduced model, a modified Newmark method that is unconditionally sta ble is proposed to integrate the responses of the reduced system. The advan tage of this method is that the nonlinear iterations only need to be execut ed on localized nonlinear parts of the system equations. The numerical Sche mes of this study are applied to a large-order flexible rotor with two elli ptical bearing supports. The periodic solutions and long term behaviors of the system are investigated numerically which reveals many interesting phen omena.