Dynamic analysis of rectangular thin plates of arbitrary boundary conditions under moving loads

• A method to treat dynamic response of plate carrying moving loads is presented.
• Rayleigh–Ritz method associated with Courant's penalty method is employed.
• Differential quadrature method is used for discretization of temporal derivatives.
• Presented technique is applicable for arbitrary edge boundary conditions.

A comprehensive method is proposed to predict the dynamic behaviors of flat plate of arbitrary boundary conditions subjected to moving loads, based on Kirchhoff plate theory. The governing equations of motion are derived using the Lagrange equation. Rayleigh–Ritz method is employed and extended to treat the spatial partial derivatives. Different with conventional Rayleigh–Ritz solutions, the admissible functions adopted here integrate the advantages of both polynomials and trigonometric functions, which just satisfy a totally unconstrained condition, and Courant's penalty method is used to handle constraints. Differential quadrature method is used for discretization of temporal derivatives. The results show that the presented method is very reliable and efficient, and its convergence and accuracy are also better compared to finite element method. Moreover, the method is good for dealing with the boundary conditions due to employing suitable admissible functions. To illustrate this, the method presented evaluates the dynamic response of a plate example, whose three edges are usual constrains, and the fourth edge connects to a real spring with arbitrary length and stiffness value.