A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

doi:10.1007/s10483-019-2549-7

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (12): 1695-1722.doi: https://doi.org/10.1007/s10483-019-2549-7

• 论文 • 下一篇

A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

Lu LU^1,2, Li ZHU³, Xingming GUO¹, Jianzhong ZHAO¹, Guanzhong LIU¹

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China;
2. Department of Mechanical Engineering, University of Alberta, Edmonton T6G 2G8, Canada;
3. School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan 411105, Hunan Province, China

收稿日期:2019-07-03 修回日期:2019-08-10 出版日期:2019-12-03 发布日期:2019-11-20
通讯作者: Xingming GUO E-mail:xmguo@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11872233 and 11472163), the China Scholarship Council (No. 201706890041), and the Innovation Program of Shanghai Municipal Education Commission (No. 2017-01-07-00-09-E00019)

A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

Lu LU^1,2, Li ZHU³, Xingming GUO¹, Jianzhong ZHAO¹, Guanzhong LIU¹

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China;
2. Department of Mechanical Engineering, University of Alberta, Edmonton T6G 2G8, Canada;
3. School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan 411105, Hunan Province, China

Received:2019-07-03 Revised:2019-08-10 Online:2019-12-03 Published:2019-11-20
Contact: Xingming GUO E-mail:xmguo@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11872233 and 11472163), the China Scholarship Council (No. 201706890041), and the Innovation Program of Shanghai Municipal Education Commission (No. 2017-01-07-00-09-E00019)

摘要/Abstract

摘要： In this paper, a novel size-dependent functionally graded (FG) cylindrical shell model is developed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory. The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical types of size effects simultaneously, which are the nonlocal stress effect, the strain gradient effect, and the surface energy effects. With the help of Hamilton's principle and first-order shear deformation theory, the non-classical governing equations and related boundary conditions are derived. By using the proposed model, the free vibration problem of FG cylindrical nanoshells with material properties varying continuously through the thickness according to a power-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various boundary conditions are obtained. After verifying the reliability of the proposed model and analytical method by comparing the degenerated results with those available in the literature, the influences of nonlocal parameter, material length scale parameter, power-law index, radius-to-thickness ratio, length-to-radius ratio, and surface effects on the vibration characteristic of functionally graded cylindrical nanoshells are examined in detail.

关键词: nonlocal strain gradient theory, surface elasticity theory, first-order shear deformation theory, vibration, functionally graded (FG) cylindrical nanoshell

Abstract: In this paper, a novel size-dependent functionally graded (FG) cylindrical shell model is developed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory. The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical types of size effects simultaneously, which are the nonlocal stress effect, the strain gradient effect, and the surface energy effects. With the help of Hamilton's principle and first-order shear deformation theory, the non-classical governing equations and related boundary conditions are derived. By using the proposed model, the free vibration problem of FG cylindrical nanoshells with material properties varying continuously through the thickness according to a power-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various boundary conditions are obtained. After verifying the reliability of the proposed model and analytical method by comparing the degenerated results with those available in the literature, the influences of nonlocal parameter, material length scale parameter, power-law index, radius-to-thickness ratio, length-to-radius ratio, and surface effects on the vibration characteristic of functionally graded cylindrical nanoshells are examined in detail.

Key words: nonlocal strain gradient theory, surface elasticity theory, first-order shear deformation theory, vibration, functionally graded (FG) cylindrical nanoshell

中图分类号:

Lu LU, Li ZHU, Xingming GUO, Jianzhong ZHAO, Guanzhong LIU. A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(12): 1695-1722.

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A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

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