An analytical procedure to study vibration of rectangular plates under non-uniform in-plane loads based on first-order shear deformation theory

In this paper, an analytical procedure is presented to study the vibrational behavior of rectangular plates subjected to different types of non-uniformly distributed in-plane loads. The prebuckling equations, which contain two coupled partial differential equations, are solved analytically by considering the in-plane constrains. The potential and kinetic energies of the plate are calculated based on the first-order shear deformation theory, and the Ritz method is used to obtain the corresponding eigenvalue problem from Hamilton's principle. By parametric study, the effects of plate aspect ratio, thickness ratio and intensity of four types of in-plane load profiles, i.e., constant, parabolic, cosine and triangular on vibrational frequency and buckling load of the plate, are investigated. Comparison of the obtained results with the finite element solution shows the accuracy of the presented method for solving similar problems.