Application of generalized differential quadrature element method to free vibration of FG-GPLRC T-shaped plates

Abstract

Application of the generalized differential quadrature element (GDQE) method is illustrated for the free vibration analysis of T-shape plates. Plate is considered as a laminated composite which every layer is reinforced with the graphene platelets (GPLs). Random orientation and uniform distribution are assumed in the combination of reinforcing particles with the matrix. Also, variation of the GPL weight fraction from one layer to another is based on four models of functionally graded (FG). The Halpin-Tsai micromechanical rule is employed to obtain the effective elasticity modulus of media. This rule considers the size and geometry of applied GPLs. First order shear deformation theory with Hamilton’s principle are implemented to derive the equations of motion. It is worth noting that the equations of motion are extracted for each divided element by means of the finite element part of GDQE. Next, the GDQ tool is used to locate the Chebyshev-Gauss-Lobatto grid points on the elements and converting the related motion differential equations into a system of algebraic equations. After satisfying the compatibility conditions between stuck elements and the external edges’ conditions, the governing eigenvalue problem is solved. Some comparison studies are carried out to demonstrate the validity and efficiency of applied method. Henceforth, several novel results are shown to understand the free vibration behaviour of T-shaped FG-GPLRC plates. Furthermore, the effects of GPL weight fraction, functionally graded patterns, boundary conditions, and geometric parameters are presented on the frequency response and corresponding mode shapes.