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2 Archives of Civil and Mechanical Engineering

2 2023

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

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Mohammad‑Rezaei Bidgoli E. , Arefi M.

2023

tom 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.

Effect of porosity and characteristics of carbon nanotube on the nonlinear characteristics of a simply-supported sandwich plate

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Bidgoli E. M.-R. , Arefi M.

2023

tom Vol. 23, no. 3

art. no. e214, 2023

This paper presents geometric-based nonlinear formulation of a composite sandwich plate on the elastic foundation based on first-order shear deformation theory. The composite sandwich plate is fabricated from a porous core integrated with two carbon-nanotubes-reinforced face sheets. After developing the kinematic relations based on first-order shear deformation theory, the geometric nonlinearity is accounted based on von-Karman-type nonlinearity. Porosity of the core is modeled based on two known models in terms of porosity coefficient. After presentation of the effective material properties of the core and the carbon nanotube reinforcement in terms of porosity coefficient, volume fraction of carbon nanotube, and basic material properties, the nonlinear governing equations are derived using Hamilton’s principle. Galerkin’s approach is applied to reduce nonlinear governing equations of motion to an ordinary time-dependent differential equation. The nonlinear frequency is analytically found based on linear frequency and initial boundary conditions. Before presentation of full numerical results, a comprehensive comparative study is presented for verification of the derivation and solution procedure. The nonlinear to linear frequency ratio is computed based on significant input parameters of porous core and carbon-nanotube-reinforced face sheets such as type of porosity, porosity coefficient, volume fraction, and type of reinforcement’s distribution.