A generalized differential quadrature-based computational model for describing free vibrations behavior of functionally graded circular plates around buckled configuration

The present study aims to examine the vibrational behavior of buckled Functionally Graded (FG) circular plates under clamped and simply-supported edge conditions. To this end, von Karman assumptions were taken into account to incorporate geometric nonlinearity into Kirchhoff plate theory and derive the nonlinear governing equations of motion using Hamilton's principle. Critical buckling load and linear natural frequencies were rst calculated using Generalized Differential Quadrature (GDQ) method. Next, the postbuckling characteristics of the circular plate were identied through direct solving of the nonlinear governing equations. Several comparative studies have conrmed the reliability of the proposed model. Finally, the fundamental natural frequency of the plate was evaluated for pre- and postbuckled congurations. This study also evaluated the effects of material property and boundary conditions on the static bifurcation diagram and natural frequency of the initial unde ected and buckled plate. According to the ndings, the trend of the fundamental natural frequency changes with the applied radial load around the pre-buckled conguration differed from the one around the buckled conguration.