Development of a High-Performance Method of Vibration Analysis for a Large-Scale Nonlinear System

（Application to Various Nonlinearities）

Abstract

A rational dimensional reduction method based on a new type of complex modal analysis is developed for the accurate analysis of a nonlinear vibration generated in a large scale structure with locally strong nonlinearity. The proposed method uses the complex constrained modes obtained by fixing the nonlinear nodes to convert the state variables of linear nodes into the modal coordinates. A small number of modal coordinates which have a significant effect on the computational accuracy of the solution are selected and used for analysis in combination with the state variables of nonlinear nodes expressed in the physical coordinates. The remaining modal coordinates which have a little effect on the computational accuracy are appropriately approximated and eliminated from the system. By using the reduced model derived by this method, not only the solution but also the stability of the solution can be computed with high speed and accurately. In this paper, in order to improve the practicality of the method, the effectiveness of the method is confirmed by applying it to a non-linearity that has not yet been applied.