Transverse Vibration and Buckling Analysis of Rectangular Plate under Arbitrary In-Plane Loads

Stresses are generated in plates under initial loads, which couple with the subsequent transverse deformation to affect the buckling and transverse vibration characteristics of plates. There exists no exact solution method for the stress field of a rectangular plate under arbitrary in-plane loads. 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. The present results are verified by comparing to existing studies and those obtained from finite element method (FEM). The effects of the magnitude and distribution of in-plane boundary stresses and boundary conditions on the dynamic characteristics and stability of the rectangular plate are analyzed. The method used in the paper has demonstrated improved convergence and accuracy with good universality.