THE ROLE OF EIGENPARAMETER GRADIENTS IN THE DETECTION OF PERTURBATIONS IN DISCRETE LINEAR SYSTEMS

Continuous mechanical systems can be characterized through analysis of discrete linear models. Such models can provide approximations for the eigenvalues and eigenvectors (collectively, “eigenparameters”). Although the eigenparameters do not qualify as measures for the state of the system in response to specific loading and boundary conditions, they do reflect the identity of the system, and this in itself has important applications. In particular, the eigenparameters can be used to study the sensitivity of a system to perturbations, due perhaps to damage incurred by one or more discrete elements. These studies can rationalize the choice and weighting of eigenparameters for system identification strategies, damage detection algorithms, and damage assessment methods. To this end, this paper develops a set of sensitivity coefficients based on gradients of the eigenparameters. Sensitivities are normalized with respect to that of the harmonic oscillator, and generalized to include the mode vectors through the definition of a figure of merit. Analytical and numerical examples based on appropriate elements are used to illustrate the utility of the approach.