Explicit eigenanalysis in structural dynamics using viscous dynamic relaxation method
Civil Engineering Department, Eqbal Lahoori Institute of Higher Education, Mashhad, Iran
2 Civil Engineering Department, Mashhad Branch, Islamic Azad University, P.O.Box. 9179156314, Mashhad, Iran
Accepted: 27 September 2022
Published online: 7 October 2022
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.