Effects of thermo-magneto-electro nonlinearity characteristics on the stability of functionally graded piezoelectric beam

doi:10.1007/s10483-020-2570-9

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (2): 313-326.doi: https://doi.org/10.1007/s10483-020-2570-9

Effects of thermo-magneto-electro nonlinearity characteristics on the stability of functionally graded piezoelectric beam

Haohao BI^1,2, Bo WANG^2,3, Zichen DENG^2,3, Shuodao WANG⁴

1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
2. Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi'an 710072, China;
3. Department of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China;
4. School of Mechanical and Aerospace Engineering, Oklahoma State University, Oklahoma 74078, U.S.A.

收稿日期:2019-08-10 修回日期:2019-11-12 发布日期:2020-01-03
通讯作者: Bo WANG E-mail:bobowang0406@gmail.com
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11802319) and the National Key Research and Development Program of China (No. 2017YFB1102801)

Effects of thermo-magneto-electro nonlinearity characteristics on the stability of functionally graded piezoelectric beam

Haohao BI^1,2, Bo WANG^2,3, Zichen DENG^2,3, Shuodao WANG⁴

1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
2. Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi'an 710072, China;
3. Department of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China;
4. School of Mechanical and Aerospace Engineering, Oklahoma State University, Oklahoma 74078, U.S.A.

Received:2019-08-10 Revised:2019-11-12 Published:2020-01-03
Contact: Bo WANG E-mail:bobowang0406@gmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11802319) and the National Key Research and Development Program of China (No. 2017YFB1102801)

摘要/Abstract

摘要： Due to the increasing interests in using functionally graded piezoelectric materials (FGPMs) in the design of advanced micro-electro-mechanical systems, it is important to understand the stability behaviors of the FGPM beams. In this study, considering the effects of geometrical nonlinearity, temperature, and electricity in the constitutive relations and the effect of the magnetic field on the FGPM beam, the Euler-Bernoulli beam model is adopted, and the nonlinear governing equation of motion is derived via Hamilton's principle. A perturbation method, which can decompose the deflection into static and dynamic components, is utilized to linearize the nonlinear governing equation. Then, a dynamic stability analysis is carried out, and the approximate analytical solutions for the nonlinear frequency and boundary frequencies of the unstable region are obtained. Numerical examples are performed to verify the present analysis. The effects of the static deflection, the static load factor, the temperature change, and the magnetic field flux on the stability behaviors of the FGPM beam are discussed. From the proposed analytical solutions and numerical results, one can easily and clearly find the effects of various controlled parameters, such as geometric and physical properties of the system, on the mechanical behaviors of structures, and the conclusions are very important and useful for the design of micro-devices.

关键词: functionally graded piezoelectric material (FGPM), geometrical nonlinearity, stability analysis

Abstract: Due to the increasing interests in using functionally graded piezoelectric materials (FGPMs) in the design of advanced micro-electro-mechanical systems, it is important to understand the stability behaviors of the FGPM beams. In this study, considering the effects of geometrical nonlinearity, temperature, and electricity in the constitutive relations and the effect of the magnetic field on the FGPM beam, the Euler-Bernoulli beam model is adopted, and the nonlinear governing equation of motion is derived via Hamilton's principle. A perturbation method, which can decompose the deflection into static and dynamic components, is utilized to linearize the nonlinear governing equation. Then, a dynamic stability analysis is carried out, and the approximate analytical solutions for the nonlinear frequency and boundary frequencies of the unstable region are obtained. Numerical examples are performed to verify the present analysis. The effects of the static deflection, the static load factor, the temperature change, and the magnetic field flux on the stability behaviors of the FGPM beam are discussed. From the proposed analytical solutions and numerical results, one can easily and clearly find the effects of various controlled parameters, such as geometric and physical properties of the system, on the mechanical behaviors of structures, and the conclusions are very important and useful for the design of micro-devices.

Key words: functionally graded piezoelectric material (FGPM), geometrical nonlinearity, stability analysis

中图分类号:

74H45

Haohao BI, Bo WANG, Zichen DENG, Shuodao WANG. Effects of thermo-magneto-electro nonlinearity characteristics on the stability of functionally graded piezoelectric beam[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(2): 313-326.

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Effects of thermo-magneto-electro nonlinearity characteristics on the stability of functionally graded piezoelectric beam

Effects of thermo-magneto-electro nonlinearity characteristics on the stability of functionally graded piezoelectric beam

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