SYMMETRIC INVERSE EIGENVALUE VIBRATION PROBLEM AND ITS APPLICATION

This paper summarises the authorsʹ previous effort on inverse eigenvalue problem for linear vibrating systems described by a vector differential equation with constant coefficient matrices and non-proportional damping. The inverse problem of interest here is that of determining real symmetric coefficient matrices assumed to represent mass normalised velocity and position coefficient matrices, given a set of specified complex eigenvalues and eigenvectors. There are given two solutions of a symmetric inverse eigenvalue problem presented by Starek and Inman [1, 2]. The theory of inverse eigenvalue problem is applied to the model updating problem. The goal of this paper is to recognise that he model updating problem is a subset of the inverse eigenvalue problem. The approach proposed here is to use the results of inverse eigenvalue problem to develop methods for model updating. Comments are made on how their procedure may be used to solve the damage detection problem.