Theoretical and Numerical Solution for the Bending and Frequency Response of Graphene Reinforced Nanocomposite Rectangular Plates

Abstract

In this work, we study the vibration and bending response of functionally graded graphene platelets reinforced composite (FG-GPLRC) rectangular plates embedded on different substrates and thermal conditions. The governing equations of the problem along with boundary conditions are determined by employing the minimum total potential energy and Hamilton’s principle, within a higher-order shear deformation theoretical setting. The problem is solved both theoretically and numerically by means of a Navier-type exact solution and a generalized differential quadrature (GDQ) method, respectively, whose results are successfully validated against the finite element predictions performed in the commercial COMSOL code, and similar outcomes available in the literature. A large parametric study is developed to check for the sensitivity of the response to different foundation properties, graphene platelets (GPL) distribution patterns, volume fractions of the reinforcing phase, as well as the surrounding environment and boundary conditions, with very interesting insights from a scientific and design standpoint.

Free vibration analysis of FG‐GPL and FG‐CNT hybrid laminated nano composite truncated conical shells using systematic differential quadrature method

“…Where𝑤 𝐺𝑃𝐿 ,𝑙 𝐺𝑃𝐿 and 𝑡 𝐺𝑃𝐿 denote the average width, length, and thickness of GPLs, while 𝐸 𝑚 is the elasticity modulus of the matrix. The effective shear modulus of an FG-GPLs layer developed by Safarpour et al [39] and calculated as:…”

“…The effective shear modulus of an FG‐GPLs layer developed by Safarpour et al. [39] and calculated as: $$$$\begin{equation} G_c^{FG - GPL}(z) = \frac{{E_c^{FG - GPL}(z)}}{{2(1 + {\nu ^{FG - GPL}}(z))}} \end{equation}$$$$…”