Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

doi:10.1007/s10483-022-2892-7

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (8): 1203-1218.doi: https://doi.org/10.1007/s10483-022-2892-7

Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

Qingdong CHAI¹, Yanqing WANG^1,2, Meiwen TENG¹

1. Key Laboratory of Structural Dynamics of Liaoning Province, College of Sciences, Northeastern University, Shenyang 110819, China;
2. Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819, China

收稿日期:2022-03-18 修回日期:2022-05-31 发布日期:2022-07-27
通讯作者: Yanqing WANG, E-mail: wangyanqing@mail.neu.edu.cn
基金资助:
the National Natural Science Foundation of China (No. 11922205) and the Fundamental Research Funds for the Central Universities of China (No. N2005019)

Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

Qingdong CHAI¹, Yanqing WANG^1,2, Meiwen TENG¹

1. Key Laboratory of Structural Dynamics of Liaoning Province, College of Sciences, Northeastern University, Shenyang 110819, China;
2. Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819, China

Received:2022-03-18 Revised:2022-05-31 Published:2022-07-27
Contact: Yanqing WANG, E-mail: wangyanqing@mail.neu.edu.cn
Supported by:
the National Natural Science Foundation of China (No. 11922205) and the Fundamental Research Funds for the Central Universities of China (No. N2005019)

摘要/Abstract

摘要： The aim of the present study is to investigate the nonlinear free vibration of spinning cylindrical shells under spinning and arbitrary boundary conditions. Artificial springs are used to simulate arbitrary boundary conditions. Sanders' shell theory is employed, and von Kármán nonlinear terms are considered in the theoretical modeling. By using Chebyshev polynomials as admissible functions, motion equations are derived with the Ritz method. Then, a direct iteration method is used to obtain the nonlinear vibration frequencies. The effects of the circumferential wave number, the boundary spring stiffness, and the spinning speed on the nonlinear vibration characteristics of the shells are highlighted. It is found that there exist sensitive intervals for the boundary spring stiffness, which makes the variation of the nonlinear frequency ratio more evident. The decline of the frequency ratio caused by the spinning speed is more significant for the higher vibration amplitude and the smaller boundary spring stiffness.

关键词: spinning cylindrical shell, nonlinear free vibration, arbitrary boundary condition, Chebyshev polynomial, Sanders' shell theory

Abstract: The aim of the present study is to investigate the nonlinear free vibration of spinning cylindrical shells under spinning and arbitrary boundary conditions. Artificial springs are used to simulate arbitrary boundary conditions. Sanders' shell theory is employed, and von Kármán nonlinear terms are considered in the theoretical modeling. By using Chebyshev polynomials as admissible functions, motion equations are derived with the Ritz method. Then, a direct iteration method is used to obtain the nonlinear vibration frequencies. The effects of the circumferential wave number, the boundary spring stiffness, and the spinning speed on the nonlinear vibration characteristics of the shells are highlighted. It is found that there exist sensitive intervals for the boundary spring stiffness, which makes the variation of the nonlinear frequency ratio more evident. The decline of the frequency ratio caused by the spinning speed is more significant for the higher vibration amplitude and the smaller boundary spring stiffness.

Key words: spinning cylindrical shell, nonlinear free vibration, arbitrary boundary condition, Chebyshev polynomial, Sanders' shell theory

中图分类号:

70J30

Qingdong CHAI, Yanqing WANG, Meiwen TENG. Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(8): 1203-1218.

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Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

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