Modified Inverse Iteration Method Using the Side Condition and the Step Length; Case 2: Multiple or Close Natural Frequencies

Abstract

An efficient numerical method which can analyze the eigenproblem for the large structural system with multiple or close eigenvalues is presented. This method is formulated by applying the accelerated Newton-Raphson method to obtained from the solution of a constrained stationary value problem. The step length used in the accelerated Newton-Raphson method is calculated by the least square concept. This method can calculate the natural frequencies and mode shapes without any numerical instability which may be often encountered in the well-known methods such as the subspace iteration method or the determinant search method which has been widely used for solving eigenvalue problem. The efficiency of this method is verified by comparing convergence and solution time for numerical examples with those of the subspace iteration method and the determinant search method.