Nonlinear free vibration of piezoelectric cylindrical nanoshells

doi:10.1007/s10483-019-2476-6

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (5): 601-620.doi: https://doi.org/10.1007/s10483-019-2476-6

Nonlinear free vibration of piezoelectric cylindrical nanoshells

Yanqing WANG^1,2, Yunfei LIU¹, J. W. ZU³

1. Department of Mechanics, Northeastern University, Shenyang 110819, China;
2. Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819, China;
3. Schaefer School of Engineering and Science, Stevens Institute of Technology, New Jersey 07030, U. S. A

收稿日期:2018-09-12 修回日期:2018-10-30 出版日期:2019-05-01 发布日期:2019-05-01
通讯作者: Yanqing WANG E-mail:wangyanqing@mail.neu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11672071) and the Fundamental Research Funds for the Central Universities (No. N170504023)

Nonlinear free vibration of piezoelectric cylindrical nanoshells

Yanqing WANG^1,2, Yunfei LIU¹, J. W. ZU³

1. Department of Mechanics, Northeastern University, Shenyang 110819, China;
2. Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819, China;
3. Schaefer School of Engineering and Science, Stevens Institute of Technology, New Jersey 07030, U. S. A

Received:2018-09-12 Revised:2018-10-30 Online:2019-05-01 Published:2019-05-01
Contact: Yanqing WANG E-mail:wangyanqing@mail.neu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11672071) and the Fundamental Research Funds for the Central Universities (No. N170504023)

摘要/Abstract

摘要：

The nonlinear vibration characteristics of the piezoelectric circular cylindrical nanoshells resting on an elastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into account. Based on the nonlocal elasticity theory and Donnell's nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived by employing Hamilton's principle. Then, the Galerkin method is used to transform the governing equations into a set of ordinary differential equations, and subsequently, the multiple-scale method is used to obtain an approximate analytical solution. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external electric potential, the temperature rise, and the Winkler-Pasternak foundation parameters on the nonlinear vibration characteristics of circular cylindrical piezoelectric nanoshells.

关键词: jets, environmental hydraulics, similarity solutions., piezoelectric cylindrical nanoshell, nonlinear vibration, multiple-scale method, size effect, nonlocal elasticity theory, Donnell's nonlinear shell theory

Abstract:

Key words: jets, environmental hydraulics, similarity solutions., nonlocal elasticity theory, piezoelectric cylindrical nanoshell, multiple-scale method, Donnell's nonlinear shell theory, nonlinear vibration, size effect

中图分类号:

74H45

Yanqing WANG, Yunfei LIU, J. W. ZU. Nonlinear free vibration of piezoelectric cylindrical nanoshells[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(5): 601-620.

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Nonlinear free vibration of piezoelectric cylindrical nanoshells

Nonlinear free vibration of piezoelectric cylindrical nanoshells

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