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

(A Rational Method for Determining the Number of Low Frequency Modes)

Abstract

A rational dimension reduction method based on a new type of complex modal analysis is developed in order to accurately analyze nonlinear vibrations generated in large-scale structures with local strong nonlinearity, non-proportional damping and asymmetric matrix at low computational cost. In the proposed method, first, the linear state variables are transformed into modal coordinates using complex constrained modes obtained by fixing nonlinear state variables. Next, a reduced model is derived by selecting a small number of modal coordinates that have a significant effect on the computational accuracy of the solution, and coupling them with the state variables of nonlinear state variables expressed in physical coordinates. In that process, the remaining modal coordinates that have little effect on the computational accuracy are appropriately approximated and integrated into the equations of motion for nonlinear state variables as correction terms. Furthermore, by using a method of estimating the effect of higher order modes from lower order modes, the computation of higher order eigenpairs becomes unnecessary. In this report, a method for determining the number of low-order modes is proposed to improve the practicality of the method, and its effectiveness is confirmed for thin plate structures.