Vibration and Wave Analyses in the Functionally Graded Graphene-Reinforced Composite Plates Based on the First-Order Shear Deformation Plate Theory

Abstract

Graphene platelets (GPLs) can be used to enhance the mechanical and electrical properties of the matrix material, which efficiently determines and improves the dynamic behavior in composite structures. Based on the first-order shear deformation theory, this paper investigates the vibration and wave problems in a functionally graded graphene-reinforced composite plate. The composite plate is composed of the polymer matrix reinforced with GPLs that are dispersed along the thickness direction, following four kinds of functionally graded patterns. The governing equation of dynamic problems in the composite plate can be described in the state space formulation, and be solved using the method of reverberation-ray matrix (MRRM). Unlike the traditional state space method, this method is unconditionally stable due to introducing the dual coordinates, which can inherently avoid the numerical instability. After a validation study to verify the present analysis, a parametric study is conducted to analyze the effect of weight fraction, size and distribution patterns of the reinforments, as well as the boundary conditions and aspect ratios on the dynamic behaviors of the composite plate, hence providing a better way to achieve improved dynamic resistances of the GPLs composite plates.