Eigensolution method for structures with multiple or close eigenvalues

Abstract

A solution method that can calculate the eigenproblem for large structures with multiple or close natural frequencies is presented. The method is formulated by the accelerated Newton-Raphson method for the transformed problem. The method can calculate the natural frequencies and mode shapes without any of the numerical instability that may be encountered in the inverse iteration process with a shift of the well-known methods, such as the subspace iteration method or the determinant search method, which have been widely used for solving an eigenproblem. The efficiency of the method is verified by comparing convergence and solution times for numerical examples with those of the subspace iteration method and the determinant search method.