MMPM for the Dynamic Analysis of Multi-Layer Connected Plates Subjected to Arbitrary-Direction Moving Loads

The Multi-layer Moving Plate Method (MMPM) is developed in this paper to investigate the dynamic behavior of a multi-layer connected plate sitting on a Pasternak foundation and subjected to arbitrary-direction moving loads. The equations of motion governing the behavior of the plate are derived based on the principle of virtual work. The governing equations are subsequently converted into the moving coordinate system and discretized using two-layer nine-node quadrilateral elements within the framework of the MMPM. The final set of equations is obtained through the application of a conventional assembly method and is subsequently solved utilizing the Newmark's β technique. The new point presented in this paper is that the load can move in any direction on the plate. Some benchmark solutions are used to verify the proposed model's results. Then, the dynamic analysis of the multi-layer connected plate is investigated under an oblique direction moving load. The obtained results point out that the magnitude of the displacement around the applied loading point is the same; however, it tends to deviate in the motion direction. The maximum displacement value is independent of the moving load's direction.