ANALYSIS OF NONLINEAR FORCED VIBRATION USING COMPONENT MODE SYNTHESIS METHOD

摘要

In this paper, an analytical approach for nonlinear forced vibration of a multi-degree-of-freedom system is proposed using the component mode synthesis method. The whole system is divided into some components and a nonlinear modal equation of each component is derived using the unconstrained vibration modes. The modal equations of all components and the conjunction conditions are solved simultaneously, and then the modal responses of components are derived. Finally, the dynamic responses of the whole system can be obtained. The degrees of freedom of modal equations can be reduced when the lower vibration modes are only adopted in each component. As a numerical example, a simple five-degree-of-freedom system is considered, in which all spring have cubic type nonlinearity. As a result, it is shown that even if the lower vibration modes of each component are only adopted, the accurate dynamic response near the first resonance can be obtained.