Nonlinear thickness-shear vibration of an infinite piezoelectric plate with flexoelectricity based on the method of multiple scales

doi:10.1007/s10483-022-2842-7

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (5): 653-666.doi: https://doi.org/10.1007/s10483-022-2842-7

Nonlinear thickness-shear vibration of an infinite piezoelectric plate with flexoelectricity based on the method of multiple scales

Yang ZHENG^1,2, Bin HUANG^1,2, Lijun YI², Tingfeng MA², Longtao XIE², Ji WANG²

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

收稿日期:2022-01-07 修回日期:2022-02-24 发布日期:2022-05-05
通讯作者: Bin HUANG, E-mail:huangbin@nbu.edu.cn;Longtao XIE, E-mail:xielongtao@nbu.edu.cn
基金资助:
the National Natural Science Foundation of China (No.11702150),the Natural Science Foundation of Zhejiang Province of China (Nos.LY20A020002 and LY21A020003),the Natural Science Foundation of Ningbo (No.202003N4015),the Project of Key Laboratory of Impact and Safety Engineering (Ningbo University),the Ministry of Education (No.CJ202009),and the Technology Innovation 2025 Program of Municipality of Ningbo (No.2019B10122)

Nonlinear thickness-shear vibration of an infinite piezoelectric plate with flexoelectricity based on the method of multiple scales

Yang ZHENG^1,2, Bin HUANG^1,2, Lijun YI², Tingfeng MA², Longtao XIE², Ji WANG²

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

Received:2022-01-07 Revised:2022-02-24 Published:2022-05-05
Contact: Bin HUANG, E-mail:huangbin@nbu.edu.cn;Longtao XIE, E-mail:xielongtao@nbu.edu.cn
Supported by:
the National Natural Science Foundation of China (No.11702150),the Natural Science Foundation of Zhejiang Province of China (Nos.LY20A020002 and LY21A020003),the Natural Science Foundation of Ningbo (No.202003N4015),the Project of Key Laboratory of Impact and Safety Engineering (Ningbo University),the Ministry of Education (No.CJ202009),and the Technology Innovation 2025 Program of Municipality of Ningbo (No.2019B10122)

摘要/Abstract

摘要： 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.

关键词: thickness-shear vibration, piezoelectric plate, size effect

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.

Key words: thickness-shear vibration, piezoelectric plate, size effect

中图分类号:

74J10

Yang ZHENG, Bin HUANG, Lijun YI, Tingfeng MA, Longtao XIE, Ji WANG. Nonlinear thickness-shear vibration of an infinite piezoelectric plate with flexoelectricity based on the method of multiple scales[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(5): 653-666.

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Nonlinear thickness-shear vibration of an infinite piezoelectric plate with flexoelectricity based on the method of multiple scales

Nonlinear thickness-shear vibration of an infinite piezoelectric plate with flexoelectricity based on the method of multiple scales

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