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Size-dependent analysis of a functionally graded piezoelectric micro-cylinder based on the strain gradient theory with the consideration of flexoelectric effect: plane strain problem

In this study, a size-dependent analysis of functionally graded piezoelectric (FGP) micro-rotating cylinder is presented based on the plane strain condition and strain gradient theory, which is a non-classical theory capable of capturing the size effect in microscaled structures. The present model i...

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Published in:Journal of the Brazilian Society of Mechanical Sciences and Engineering 2020-08, Vol.42 (8), Article 410
Main Authors: Dini, Ali, Shariati, Mahmoud, Zarghami, Fatemeh, Nematollahi, Mohammad Amin
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description In this study, a size-dependent analysis of functionally graded piezoelectric (FGP) micro-rotating cylinder is presented based on the plane strain condition and strain gradient theory, which is a non-classical theory capable of capturing the size effect in microscaled structures. The present model is used to analyze the FGP micro-rotating cylinder with the consideration of flexoelectric effects exposed to a symmetric magneto-electro-mechanical loading. All mechanical and electrical properties are assumed to be graded in the thickness direction according to a power-law distribution. With respect to the fifth-order strain gradient coefficient and electromechanical coupling, the constitutive equations are obtained from electric Gibbs free energy density, which is a function of strain, second-order deformation gradient and electric field. By substituting the constitutive equations in electric and mechanical equilibrium equations, two coupled electromechanical governing differential equations in terms of radial displacement and electric potential are derived considering centrifugal force and Lorentz magnetic force obtained from Maxwell’s relations. The generalized differential quadrature method is proposed to solve the coupled governing differential equations. Numerical results attained from the strain gradient elasticity reveal the effects of flexoelectric, microstructural length scale, non-homogeneity constant, rotation and magnetic field on the response of the FGP micro-rotating cylinder.
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1806-3691
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subjects Centrifugal force
Constitutive equations
Constitutive relationships
Differential equations
Electric fields
Electrical properties
Engineering
Equilibrium equations
Flux density
Generalized differential quadrature method
Gibbs free energy
Homogeneity
Magnetic fields
Magnetic properties
Mechanical Engineering
Piezoelectricity
Plane strain
Quadratures
Rotating cylinders
Rotation
Size effects
Technical Paper
title Size-dependent analysis of a functionally graded piezoelectric micro-cylinder based on the strain gradient theory with the consideration of flexoelectric effect: plane strain problem
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