Explicit eigenanalysis in structural dynamics using viscous dynamic relaxation method

This paper introduces a novel application of the dynamic relaxation (DR) method with viscous damping for solving eigenvalue problems arising from finite element simulation of structural dynamics. The scheme is a simple vector iteration solver based on the fundamental concepts of structural dynamics, which has been successfully employed in various applications of computational mechanics, including linear and nonlinear, form findings, buckling, and dynamic analyses. However, the potentiality of the method in solving eigenvalue problems in structural dynamics has not been investigated yet. The present work attempts to generalize the DR algorithm for tackling partial eigenproblems in vibration analysis. For analysis of higher modes, DR is supplemented by a simple mode purification procedure. Some numerical examples are solved via the suggested algorithm and comparisons are also made with other published results. The method is simple, easy to grasp, and only uses matrix-vector multiplications.