Vibration of a rectangular plate undergoing forces moving along a circular path

Abstract

A rectangular plate subjected to the curvilinear moving loads is a practical engineering problem. Nevertheless, the literature concerning the dynamic characteristics of a flat plate undergoing forces moving along a circular path is not found so far. For this reason, the title problem is studied. In general, in order to tackle a problem with the finite element method (FEM), all the external loads on a structural system must be replaced by the equivalent forces (and moments) applied at the associated nodes first and then the equation of motion for the entire system with the last equivalent nodal forces (and moments) as the excitation mechanism was solved. Therefore, the formulations for calculating the instantaneous positions of the moving loads and the expressions for transforming the external loads into the equivalent nodal forces (and moments) on the structure are presented, and the dynamic responses of a rectangular plate subjected to multiple forces moving along a circular path were determined. The key point of this paper is to investigate the influence of the following parameters on the dynamic responses of the rectangular plate: supporting conditions of the plate, rotating speed of the moving loads, radius of the circular path and total number of the moving loads. It is hoped that the presented formulations will be significant for solving the title problem and the presented results will be helpful for looking into the associated phenomena or designing the similar systems.