重庆工商大学学报（自然科学版）2024，Vol.41Issue(4)：36-44,9.DOI:10.16055/j.issn.1672-058X.2024.0004.005
材料梯度、几何非线性和高阶剪切效应对压电纳米梁力电特性的耦合影响
Coupling Effects of Material Gradient,Geometric Nonlinearity and High-order Shear Effect on the Electro-mechanical Properties of Piezoelectric Nanobeam
摘要
Abstract
Objective Piezoelectric materials are widely used in MEMS/NEMS due to their excellent electromechanical properties.A mathematical model of functionally graded piezoelectric(FGP)nanobeams including the flexoelectric effect and the piezoelectric effect was proposed to solve the problem that the flexoelectric effect and shear effect of piezoelectric materials at the microscale/nanoscale are neglected in the current calculation of the electromechanical response of piezoelectric nanostructures.The nanobeam consists of a piezoelectric layer and a functionally graded layer,while the materials of the functionally graded layer follow the power-law exponential distribution.Methods Firstly,based on Reddy's third-order shear deformation theory,nonlocal strain gradient theory(NSGT),Hamilton's principle,and Von K6.rm6n geometric nonlinearity,the nonlinear electromechanical coupling governing equations and corresponding boundary conditions of the gradient beam were obtained.Then,the linear frequency,nonlinear natural frequency,and the root mean square(RMS)output voltage of the simply supported beam were obtained by combining the Runge-Kutta method and the Galerkin method.Results The presented model in this study was verified by existing literature results.In addition,the numerical results showed that flexoelectric constants,piezoelectric constants,strain gradient parameters,nonlocal parameters,power-law index,and geometric dimensions have an impact on the nonlinear natural frequency and RMS voltage.Conclusion Compared with the Euler beam theory and Timoshenko beam theory,the gradient beam with the same mass has higher RMS voltage and lower nonlinear natural frequency when using Reddy's third-order shear deformation theory.关键词
非线性振动/Reddy三阶剪切变形理论/功能梯度/压电/挠曲电Key words
nonlinear vibration/Reddy's third-order shear deformation theory/functional gradient/piezoelectricity/flexoelectricity分类
数理科学引用本文复制引用
虞志勇,曾汕,罗思贵..材料梯度、几何非线性和高阶剪切效应对压电纳米梁力电特性的耦合影响[J].重庆工商大学学报（自然科学版）,2024,41(4):36-44,9.基金项目
江西省自然科学基金资助项目(20202BAB211005). （20202BAB211005）
