Nonlinear thickness-shear vibration of an infinite piezoelectric plate with flexoelectricity based on the method of multiple scales |
| |
Authors: | Yang ZHENG Bin HUANG Lijun YI Tingfeng MA Longtao XIE Ji WANG |
| |
Affiliation: | 1. Key Laboratory of Impact and Safety Engineering, Ministry of Education, Ningbo University, Ningbo 315211, Zhejiang Province, China;2. Piezoelectric Device Laboratory, Faculty of Mechanical Engineering & Mechanics, Ningbo University, Ningbo 315211, Zhejiang Province, China |
| |
Abstract: | This paper presents a nonlinear thickness-shear vibration model for onedimensional infinite piezoelectric plate with flexoelectricity and geometric nonlinearity. The constitutive equations with flexoelectricity and governing equations are derived from the Gibbs energy density function and variational principle. The displacement adopted here is assumed to be antisymmetric through the thickness due to the thickness-shear vibration mode. Only the shear strain gradient through the thickness is considered in the present model. With geometric nonlinearity, the governing equations are converted into differential equations as the function of time by the Galerkin method. The method of multiple scales is employed to obtain the solution to the nonlinear governing equation with first order approximation. Numerical results show that the nonlinear thickness-shear vibration of piezoelectric plate is size dependent, and the flexoelectric effect has significant influence on the nonlinear thickness-shear vibration frequencies of micro-size thin plates. The geometric nonlinearity also affects the thickness-shear vibration frequencies greatly. The results show that flexoelectricity and geometric nonlinearity cannot be ignored in design of accurate high-frequency piezoelectric devices. |
| |
Keywords: | thickness-shear vibration piezoelectric plate size effect |
|
| 点击此处可从《应用数学和力学(英文版)》浏览原始摘要信息 |
|
点击此处可从《应用数学和力学(英文版)》下载全文 |
|