Vibration of laminated composite quadrilateral plates reinforced with graphene nanoplatelets using the element-free IMLS-Ritz method

Abstract

This paper investigates free vibration of graphene nanoplatelet (GPL) reinforced laminated composite quadrilateral plates using the element-free IMLS-Ritz method. The effective material properties including Young's modulus, mass density and Poisson's ratio are determined by the modified Halpin–Tsai model and rule of mixture. The first-order shear deformation theory (FSDT) is employed for formulation of the energy functional. Based on the IMLS-Ritz approximation, the discrete vibration equation of the laminated composite quadrilateral plates is derived. The accuracy of the IMLS-Ritz results is examined by comparing with the published values. A comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern, geometry and size of GPL reinforcements, total number of layers and geometric parameters of quadrilateral plates on the natural frequencies of GPL reinforced laminated composite quadrilateral plate.