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

Document Type : Research Note


1 Department of Mechanical Engineering, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

2 Laboratory Unit, Stam Sanat Company, Karaj, Iran

3 Department of Mechanical Engineering, University of Kurdistan, Sanandaj, Iran

4 Department of Mechanical Engineering, Ahrar Institute of Technology and Higher Education, Rasht, Iran


In the present article, the vibrational behavior of buckled functionally graded (FG) circular plates with clamped and simply-supported edge conditions is described. Considering von Kármán’s assumptions, the geometric nonlinearity is incorporated into the Kirchhoff plate theory and the nonlinear governing equations of motion are then derived using Hamilton’s principle. Critical buckling load and linear natural frequencies are first calculated using the generalized differential quadrature (GDQ) method. Afterward, the postbuckling characteristics of the circular plate are obtained via solving the nonlinear governing equations, directly. By several comparative studies, the reliability of the presented model is revealed. Finally, the fundamental natural frequency of the plate is evaluated for prebuckled and postbuckled configurations. The effects of material property and boundary conditions on the static bifurcation diagram and the natural frequency of the initial undeflected and bucked plate are studied. It is found that the trend of the fundamental natural frequency changes with the applied radial load around the prebuckled configuration is unlike the one around the buckled configuration.


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