Large amplitude free flexural vibration analysis of finite element modeled FGM plates using new hyperbolic shear and normal deformation theory

In this paper, displacement based new hyperbolic higher-order shear and normal deformation theory (HHSNDT) is introduced for the geometrically nonlinear vibrations response of FGM plates. The proposed theory accounts for nonlinear in-plane and transverse displacement through the plate thickness. Unlike any other theory, the number of unknown functions involved in the present theory is only four, as against five or higher in the case of other well-known shear deformation theories. It also accounts the stretching effects across the thickness and does not require any shear correction factor. The fundamental equations of FGM plate are obtained using variational principle and von Karman theory is employed for large transverse deflection. Voigt and Mori-Tanaka model is used with the conjunction of exponential law and power law to estimate the graded material properties. The accuracy of the present theory is ascertained by comparing it with various available results in the literature. A comprehensive numerical study is carried out based on the present theory to examine the influence of the homogenization techniques, geometrical parameter, amplitude ratio and boundary conditions on the vibration response of the graded plate.