Dynamic analysis of a rectangular plate subjected to a mass moving with variable velocity on a predefined path or an arbitrary one

Abstract

Abstract In this research, the dynamic behavior of a thin rectangular plate subjected to a mass moving with variable velocity is studied. In previous studies, the main focus was on the vibration analysis of the structure, while there are many cases in which mass-structure interaction and how the motion of the mass is affected by the structure is of great importance. Three coupled nonlinear equations governing the motion of the mass and the transverse displacement of the plate are obtained. In general, the coordinates of the moving mass and the transverse displacement of the plate are the unknown variables. The partial differential equations are discretized using the Galerkin decomposition method and then solved numerically. Two general cases are considered in which the mass moves on a predefined path or an arbitrary one. In the first case, the equations of motion are solved for the straight and circular paths and the force needed to maintain this constraint are obtained. The effect of friction force is also investigated for both paths. In the second case, path determination is the aim. First, the effect of the deflection on the magnitude and direction of the velocity of the mass is studied. It is confirmed that the deflection of the plate can greatly affect the motion of the mass. Additionally, a spring is attached to the mass on one end and connected to a specific point on the plate on the other end. The motion of the mass and dynamics of the plate is analyzed in this case.