Vibrations of Point-Supported Rectangular Thin Plate Subjected to a Moving Force

In this paper, the dynamic behaviour of a rectangular thin plate simply supported on all edges and point supported within its region is investigated. The problem is solved by replacing this type of structure with a simply supported plate subjected to a given moving load and redundant forces situated in positions of intermediate point supports. Redundant forces are obtained by solving Volterra integral equations of the first order, which are compatibility equations corresponding to each redundant. Solutions for a simply supported plate loaded with a moving point force and concentrated time-varying force are given. Difficulties of solving Volterra integral equations analytically are bypassed by applying a simple numerical procedure. Finally, a numerical example of a plate with two point supports is presented in order to show the effectiveness of the presented method.