Modified sturm sequence property for damped systems

Abstract

Most of the eigenvalue analysis methods for the undamped or proportionally damped systems use the well-known Sturm sequence property to check the missed eigenvalues when only a set of the lowest modes is to be used for large structures. However, in the case of the non-proportionally damped systems such as the soil-structure interaction system, the structural control system and the composite structures, no counterpart of the Sturm sequence property for undamped systems has been developed yet. Hence, when some important modes are missed for those systems, it may lead to poor results in dynamic analysis. In this study, a numerical method for calculating the number of eigenvalues in an open disk of arbitrary radius for the eigenproblem with a damping matrix is proposed by applying Gleyse’s theorem. To verify the applicability of the proposed method, two numerical examples are considered.