An Efficient Algebraic Method for the Computation of Natural Frequency and Mode Shape Sensitivities, Part I: Distinct Natural Frequencies

Abstract

This paper presents an efficient numerical method for the computation of eigenpair derivatives for the real symmetric eigenvalue problem with distinct eigenvalues. The method has a very simple algorithm and gives an exact solution because no iteration scheme is used. The eigenpair derivatives can be obtained by solving algebraic equations with a symmetric coefficient matrix. The algorithm preserves the symmetry and band of the matrices, allowing efficient computer storage and solution techniques. The results of the proposed method for calculating the eigenpair derivatives are compared to those of Rudisill and Chu's method and Nelson's method, which is an efficient one in the case of distinct eigenvalues. Data is presented showing the amount of CPU time used to compute the first 10 eigenpair derivatives. The numerical stability of the proposed method is proved. As an example, to demonstrate the efficiency of the proposed method in the case of distinct eigenvalues, a cantilever plate is considered. The design parameter of the cantilever plate is its thickness. Copyright (C) 1996 Elsevier Science Ltd.