Transverse vibration and buckling analysis of rectangular plate under arbitrary in-plane loads (Q6133514)

In this paper, the stress field of a rectangular plate under arbitrary in-plane loads is solved based on the principle of minimum potential energy. The stress function is decomposed into homogeneous and special solutions. The homogeneous solution is represented by the Chebyshev polynomial while the special solution is expanded by the Fourier series. Then, the Ritz method is used to analyze the transverse vibration and buckling characteristics of the rectangular plate. The product of the boundary function and Chebyshev polynomial is used to build the vibration mode function. Effect of load spacing on vibration and buckling is studied in detail. The frequency of the rectangular plate under different boundary conditions is considered with external load local distribution in the form of centrally loaded, 3000 kN/m2, and the loading range is 0.1 m. The effect of load spacing on vibration and buckling is also studied in detail. Extensive numerical results are presented both in tabular and graphical form for direct use by practicing engineers. An interesting and useful contribution.