Natural frequency and mode shape sensitivities of damped systems: Part I, Distinct natural frequencies

A procedure for determining the sensitivities of the eigenvalues and eigenv ectors of damped vibratory systems with distinct eigenvalues is presented. The eigenpair derivatives,of the structural and mechanical damped systems c an 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. F urthermore, the method can find the exact solutions. As an example of a str uctural system to verify the proposed method and its possibilities in the c ase of the proportionally damped system, the finite element model of a cant ilever 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 param eter 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 pro posed method is that its numerical stability is established. (C) 1999 Acade mic Press.