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Nonlinear vibration analysis of sandwich plates with honeycomb core and graphene nanoplatelet‑reinforced face‑sheets

Mohammad‑Rezaei Bidgoli E., Arefi Mohammad

Archives of Civil and Mechanical Engineering

2023

Vol. 23, no. 1

art. no. e56, 2023

This paper studies nonlinear vibration analysis of a graphene nanoplatelets’ composite sandwich. The core and two face-sheets of composite sandwich plate are fabricated from a honeycomb material and graphene nanoplatelet (GNP) reinforcements, respectively. Displacement field of sandwich plate is developed based on first-order shear deformation theory. Geometric nonlinearity is accounted in the constitutive relations based on von-Karman assumptions. After derivation of the governing partial differential motion equations through Hamilton’s principle, Galerkin’s approach is used to reduce them into a nonlinear equation of motion in terms of transverse defection. The nonlinear frequency is found based on linear frequency and initial conditions, analytically. The nonlinear-to-linear frequency ratio is computed based on significant input parameters of honeycomb structure and graphene nanoplatelets such as thickness-to-length and thickness-to-height ratios, angle of honeycomb, various distribution, weigh fraction and geometric characteristics of graphene nanoplatelets. Before presentation of full numerical results, the comprehensive comparative study is presented for verifcation of the derivation and solution method.

Frequency study of functionally graded multilayer graphene platelet-reinforced polymer cylindrical panels

Farsadi T., Asadi D., Kurtaran H.

Archives of Mechanics

2021

Vol. 73, nr 5-6

471--498

In this study, nonlinear fundamental natural frequencies of Functionally Graded (FG) multilayer Graphene Platelet-reinforced Polymer Composite (GPL-RPC) curved cylindrical panels are studied. It is considered that the Graphene Platelet (GPL) nanofillers are distributed in the matrix either uniformly or nonuniformly along the thickness direction. Four GPL distribution patterns namely, UD, FG-O, FG-X, and FG-A are considered. The effective material properties of GPL-RPC layers are obtained via the modified Halpin–Tsai micromechanics model and the rule of the mixture. A nonlinear structural model is utilized based on the virtual work principle. Green’s nonlinear kinematic strain relations are used to account for the geometric nonlinearities and the First-order Shear Deformation Theory (FSDT) is adopted to generalize the formulation for the case of moderately thick cylindrical panels including transverse shear deformations. The Generalized Differential Quadrature (GDQ) method of solution is employed to solve the nonlinear governing equations of motion. The present study aims to study the effect of GPL weight fraction for the proposed distribution patterns on the nonlinear fundamental frequency of functionally graded GPL-RPC cylindrical panels with different boundary conditions.