Free vibration analysis of FG-GPLRC L-shaped plates implementing GDQE approach

Abstract

In the current research, application of generalized differential quadrature element (GDQE) method is presented to analyze the free vibration of L-shaped plates. It is considered that the laminated composite plate is reinforced by graphene platelets (GPLs). Furthermore, the GPLs are randomly oriented and uniformly dispersed in each lamina. The GPL weight fraction changes from layer to layer based on the four functionally graded models. To develop the formulation, the effective Young modulus is calculated by means of the Halpin–Tsai micromechanical rule. GDQE method firstly divides total plate domain into three rectangular elements. First order shear deformation theory (FSDT) is employed to estimate the displacement components of each element. Moreover, the Hamilton principle is utilized to extract the motion equations of elements individually. The GDQ tool is applied to each element for separating these regions into sample grid points. Properly applying the compatibility conditions between the elements is a very important factor in the correctness and accuracy of the response. In order to present the validity and accuracy of the outcomes, results are compared with the existing information in the open literature. After that, novel results are demonstrated to examine the effects of GPL weight fraction and distribution, plate geometrical parameters and various boundary conditions on the natural frequencies and corresponding mode shapes of L-shaped plates.