Optimal Placement of Viscoelastic Vibration Dampers for Kirchhoff Plates Based on PSO Method

Materials (Basel). 2021 Nov 3;14(21):6616. doi: 10.3390/ma14216616.

Abstract

The main subject of this study is to determine the optimal position of a fixed number of viscoelastic dampers on the surface of a thin (Kirchhoff-Love) plate. It is assumed that the dampers are described according to the generalized Maxwell model. In order to determine the optimal position of the dampers, a metaheuristic optimization method is used, called the particle swarm optimization method. The non-dimensional damping ratio of the first mode of the plate vibrations is assumed as an objective function in the task. The dynamic characteristics of the plate with dampers are determined by solving the non-linear eigenproblem using the continuation method. The finite element method is used to determine the stiffness matrix and the mass matrix occurring in the considered eigenproblem. The results of exemplary numerical calculations are also presented, where the final optimal arrangement of dampers on the surface of sample plates with different boundary conditions is shown graphically.

Keywords: continuation method; finite element method; non-dimensional damping ratio; optimal placement of dampers; particle swarm optimization; thin plates; viscoelastic vibration dampers.