Large amplitude free flexural vibration analysis of shear deformable FGM plates using nonlinear finite element method

In this paper, large amplitude free flexural vibration analysis of shear deformable functionally graded material (FGM) plates are investigated. The material properties of the FGM plates are assumed to vary through the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents. The nonlinear finite element equations are obtained using higher order shear deformation theory with a special modification in the transverse displacement. The Green–Lagrange nonlinear strain–displacement relation with all higher order nonlinear strain terms is included in the formulation to account for the large deflection response of the plate. The fundamental equations are obtained using variational approach by employing traction free boundary conditions on the top and bottom faces of the plate. Results are obtained by employing an efficient C0 finite element with 13 degrees of freedom (DOFs) per node. Convergence tests and comparison studies have been carried out to establish the efficacy of the present model. The variation of nonlinear frequency ratio with the amplitude ratio is highlighted for different thickness ratios, aspect ratios and volume fraction index with different boundary conditions.