Natural Frequency and Mode Shape Sensitivities of Damped System, Part I: Distinct Natural Frequencies

Abstract

A procedure for determining the sensitivities of the eigenvalues and eigenvectors of damped vibratory systems with distinct eigenvalues is presented. The eigenpair derivatives,of the structural and mechanical damped systems can be obtained consistently by solving algebraic equations with a symmetric coefficient matrix whose order is (n + 1) x (n + 1), where n is the number of co-ordinates. The algorithm of the method is very simple and compact. Furthermore, the method can find the exact solutions. As an example of a structural system to verify the proposed method and its possibilities in the case of the proportionally damped system, the finite element model of a cantilever plate is considered, and also a 7-DOF half-car model as a mechanical system in the case of a non-proportionally damped system. The design parameter of the cantilever plate is its thickness, and the design parameter of the car model is a spring. One of the remarkable characteristics of the proposed method is that its numerical stability is established. (C) 1999 Academic Press.