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

(Application to the Consistent Mass Model)

Abstract

A rational method of dimensional reduction is developed in order to analyze accurately a nonlinear vibration generated in a large-scale structure with locally strong nonlinearity, asymmetry and non-proportional damping. In the proposed method, the state variables of linear nodes are transformed into the modal coordinates by using the complex constrained modes that is obtained by fixing the nonlinear nodes, and a small number of modal coordinates that have a significant effect on the computational accuracy of the solution are selected and utilized in the analysis by combining them with the state variables of nonlinear nodes that are expressed in the physical coordinates. The remaining modes that have little effect on the computational accuracy are appropriately approximated and are eliminated from the system. From the reduced model constructed by these procedures, the steady state periodic solution and the stability, the transient solution and the quasi-periodic solution can be computed with a very high degree of computational accuracy and at a high computational speed. The effectiveness of the proposed method is verified by the computational results obtained for a straight-line beam structure modeled by FEM acting non-proportional damping with nonlinear supports.