Eigenvalue-counting methods for non-proportionally damped systems

Abstract

This paper presents numerical methods of counting the number of eigenvalues for non-proportionally damped system in some interested regions on the complex plane. Most of the eigenvalue analysis methods for proportionally damped systems use the well-known Sturm sequence property to check the missed eigenvalues when only a set of the lowest modes is used. However, in the case of the non-proportionally damped systems such as the soil-structure interaction system, the structural control system and composite structures, no counterpart of the Sturm sequence property for undamped systems has been established yet. In this study, a numerical method based on argument principle is explained with emphasis on the discretization of the contour and a new method based on Gleyse's theorem is proposed. To verify the applicability of the methods, two numerical examples are considered. (C) 2003 Elsevier Ltd. All rights reserved.