A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates

This paper presents a new shear deformation theory including the stretching effect for free vibration of the simply supported functionally graded plates. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded plate without using shear correction factors. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The present one has a new displacement field which introduces undetermined integral variables. The equation of motion of the vibrated structure obtained via the classical Hamilton's principle and solved using Navier's steps. The validation of the proposed theoretical model is performed to demonstrate the efficacy of the model. It can be concluded that the present theory is not only accurate but also simple in predicting the natural frequencies of functionally graded plates with stretching effect.