Vibration of an initially stressed rectangular plate due to an accelerated traveling mass

Abstract

This paper presents a combined application of the Ritz method, the Differential Quadrature (DQ) method, and the Integral Quadrature (IQ) method to vibration problem of rectangular plates subjected to accelerated traveling masses. In this study, the Ritz method with beam eigenfunctions is first used to discretize the spatial partial derivatives with respect to a co-ordinate direction of the plate. The DQ and IQ methods are then employed to analogize the resultant system of partial differential equations. The resulting system of ordinary differential equations is then solved by using the Newmark time integration scheme. The mixed scheme combines the simplicity of the Ritz method and high accuracy and efficiency of the DQ method. The accuracy of the proposed method is demonstrated by comparing the calculated results with those of the existing literature. It is shown that highly accurate results can be obtained using a small number of Ritz terms and DQM sampling points. Finally, the effects of following parameters having something to do with the title problem are investigated: moving load speed and acceleration, and transverse inertia of the moving load. Numerical results show that all the above-mentioned parameters have significant effects on the transient response of such structures under traveling dynamic loads.