| 摘要: |
| 目的 压电材料由于其优越的力电性能在 MEMS / NEMS 得到广泛应用。 针对目前对压电纳米结构力电响应
计算忽视了微/ 纳米尺度下压电材料的挠曲电效应以及剪切效应问题,提出了囊括挠曲电效应和压电效应的功能
梯度压电(Functionally Graded Piezoelectric,FGP)纳米梁数学模型。 纳米梁由压电层和功能梯度层组成,其中功能
梯度层材料遵循幂律指数分布。 方法 首先,基于 Reddy 三阶剪切变形理论、非局部应变梯度理论(NGST)和哈密顿
原理,并考虑了 Von Kármán 几何非线性,获得了梯度梁的非线性力电耦合控制方程及相应的边界条件;然后结合
Runge-Kutta 方法和 Galerkin 方法得到了简支梁的线性和非线性固有频率以及均方根(RMS)输出电压。 结果 提出
的模型与已有文献结果对比十分吻合。 此外,数值结果表明挠曲电常数、压电常数、应变梯度尺度参数、非局部参
数、幂律指数和几何尺寸对非线性固有频率和均方根电压有影响。 结论 相较于 Euler 梁理论和 Timoshenko 梁理
论,采用 Reddy 三阶剪切变形理论得到的梯度梁在相同质量下具有更高的 RMS 电压,同时会降低非线性固有
频率。 |
| 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 |
| DOI： |
| 分类号: |
| 基金项目: |
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| Coupling Effects of Material Gradient Geometric Nonlinearity and High-order Shear Effect on the Electromechanical Properties of Piezoelectric Nanobeam |
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YU Zhiyong； ZENG Shan ；LUO Sigui
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School of Aircraft Engineering Nanchang Hangkong University Nanchang 330063 China
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| 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
Kármán 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 Reddys third-order shear
deformation theorK. |
| Key words: nonlinear vibration Reddy's third-order shear deformation theory functional gradient piezoelectricity flexoelectricity |
