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

• Published in: Journal of the Brazilian Society of Mechanical Sciences and Engineering Vol. 42; no. 8
• Main Authors: Dini, Ali, Shariati, Mahmoud, Zarghami, Fatemeh, Nematollahi, Mohammad Amin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2020; Springer Nature B.V
• 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; Generalized differential quadrature method; Functionally graded piezoelectric material; Strain gradient elasticity; Flexoelectric effects; Lorentz force; Micro-rotating cylinder
• ISSN: 1678-5878; 1806-3691
• DOI: 10.1007/s40430-020-02497-x

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.