An assessment of a non-polynomial based higher order shear and normal deformation theory for vibration response of gradient plates with initial geometric imperfections

In the present study, a new non-polynomial based higher order shear and normal deformation theory is proposed and implemented for the vibration response of geometrically imperfect functionally graded material (FGM) plates. The present theory accounts for nonlinear variation in the in-plane and transverse displacements, respectively in the thickness coordinate. This theory contains the trigonometric shear strain shape functions and having only four unknowns in the displacement field. It is variationally consistent and accommodates thickness stretching effects without employing shear correction factor. Two micromechanics models (Mori-Tanaka and Voigt) have been employed to determine the effective material properties of the plate, and are graded continuously through the thickness direction according to a simple power law and exponential law. The accuracy and efficiency of the proposed theory have been conferred by comparing the results with an existing 3D exact solution and various higher order theories. Frequency parameters with various side-to-thickness ratios, boundary conditions, imperfection sizes, volume fraction indexes and exponential indexes have been computed for perfect and imperfect FGM plate. It is found that the proposed theory is not only accurate but also simple in predicting the free vibration responses of functionally graded ceramic-metal plates.