The role of eigenparameter gradients in the detection of perturbations in discrete linear systems

Continuous mechanical systems can be characterized through analysis of disc rete linear models. Such models can provide approximations for the eigenval ues and eigenvectors (collectively, "eigenparameters"). Although the eigenp arameters do not qualify as measures for the state of the system in respons e to specific loading and boundary conditions, they do reflect the identity of the system, and this in itself has important applications. In particula r, the eigenparameters can be used to study the sensitivity of a system to perturbations, due perhaps to damage incurred by one or more discrete eleme nts. These studies can rationalize the choice and weighting of eigenparamet ers for system identification strategies, damage detection algorithms, and damage assessment methods. To this end, this paper develops a set of sensit ivity coefficients based on gradients of the eigenparameters. Sensitivities are normalized with respect to that of the harmonic oscillator, and genera lized to include the mode vectors through the definition of a figure of mer it. Analytical and numerical examples based on appropriate elements are use d to illustrate the utility of the approach. (C) 2000 Academic Press.