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Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

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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.

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Funding

Project supported by the National Natural Science Foundation of China (No. 11922205) and the Fundamental Research Funds for the Central Universities of China (No. N2005019)

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Authors and Affiliations

  1. Key Laboratory of Structural Dynamics of Liaoning Province, College of Sciences, Northeastern University, Shenyang, 110819, China

    Qingdong Chai, Yanqing Wang & Meiwen Teng

  2. Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, 110819, China

    Yanqing Wang

Authors
  1. Qingdong Chai
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  2. Yanqing Wang
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  3. Meiwen Teng
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Corresponding author

Correspondence to Yanqing Wang.

Additional information

Citation: CHAI, Q. D., WANG, Y. Q., and TENG, M. W. Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions. Applied Mathematics and Mechanics (English Edition), 43(8), 1203–1218 (2022) https://doi.org/10.1007/s10483-022-2892-7

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Chai, Q., Wang, Y. & Teng, M. Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions. Appl. Math. Mech.-Engl. Ed. 43, 1203–1218 (2022). https://doi.org/10.1007/s10483-022-2892-7

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  • DOI: https://doi.org/10.1007/s10483-022-2892-7

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Chinese Library Classification

2010 Mathematics Subject Classification

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