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.

在这项研究中，基于平面应变条件和应变梯度理论，提出了功能梯度压电（FGP）微旋转圆柱体的尺寸依赖性分析，这是一种能够捕捉微尺度结构中尺寸效应的非经典理论。本模型用于分析FGP微旋转圆柱体，并考虑了暴露于对称磁电机械载荷下的柔电效应。假定所有机械和电气特性均根据幂律分布在厚度方向上分级。关于五阶应变梯度系数和机电耦合，从电吉布斯自由能密度获得本构方程，该电吉布斯自由能密度是应变，二阶变形梯度和电场的函数。通过将本构方程代入电气和机械平衡方程，考虑到麦克斯韦关系得到的离心力和洛伦兹磁力，得出了两个在径向位移和电势方面耦合的机电控制微分方程。提出了广义微分求积法求解耦合控制微分方程。从应变梯度弹性获得的数值结果揭示了挠性电，微结构长度尺度，非均匀性常数，旋转和磁场对FGP微旋转圆柱体响应的影响。考虑到麦克斯韦关系得到的离心力和洛伦兹磁力，推导了两个在径向位移和电势方面耦合的机电控制微分方程。提出了广义微分求积法求解耦合控制微分方程。从应变梯度弹性获得的数值结果揭示了挠性电，微结构长度尺度，非均匀常数，旋转和磁场对FGP微旋转圆柱体响应的影响。考虑到麦克斯韦关系得到的离心力和洛伦兹磁力，推导了两个在径向位移和电势方面耦合的机电控制微分方程。提出了广义微分求积法求解耦合控制微分方程。从应变梯度弹性获得的数值结果揭示了挠性电，微结构长度尺度，非均匀性常数，旋转和磁场对FGP微旋转圆柱体响应的影响。