Symmetric inverse eigenvalue vibration problem and its application

This paper summarises the authors' previous effort on inverse eigenvalue pr oblem for linear vibrating systems described by a Vector differential equat ion with constant coefficient matrices and non-proportional damping. The in verse problem of interest here is that of determining real symmetric coeffi cient matrices assumed to represent mass normalised velocity and position c oefficient matrices, given a set of specified complex eigenvalues and eigen vectors. There are given two solutions of a symmetric inverse eigenvalue pr oblem presented by Starek and Inman [1,2]. The theory of inverse eigenvalue problem is applied to the model updating p roblem. The goal of this paper is to recognise that the model updating prob lem is a subset of the inverse eigenvalue problem. The approach proposed he re is to use the results of inverse eigenvalue problem to develop methods f or model updating. Comments are made on how their procedure may be used to solve the damage de tection problem. (C) 2001 Academic Press.