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Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (3): 345-356.doi: https://doi.org/10.1007/s10483-012-1554-6

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Natural frequencies of rotating functionally graded cylindrical shells

项松1,2 李广超3 张魏3 杨明绥3   

  1. 1. Liaoning Key Laboratory of General Aviation, Shenyang Aerospace University, Shenyang 110136, P. R. China;
    2. Liaoning General Aviation Academy, Shenyang 110136, P. R. China;
    3. School of Power and Energy Engineering, Shenyang Aerospace University, Shenyang 110136, P. R. China
  • 收稿日期:2011-07-15 修回日期:2012-01-12 出版日期:2012-03-02 发布日期:2012-03-01

Natural frequencies of rotating functionally graded cylindrical shells

 XIANG Song1,2, LI Guang-Chao3, ZHANG Wei3, YANG Ming-Rui3   

  1. 1. Liaoning Key Laboratory of General Aviation, Shenyang Aerospace University, Shenyang 110136, P. R. China;
    2. Liaoning General Aviation Academy, Shenyang 110136, P. R. China;
    3. School of Power and Energy Engineering, Shenyang Aerospace University, Shenyang 110136, P. R. China
  • Received:2011-07-15 Revised:2012-01-12 Online:2012-03-02 Published:2012-03-01

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被引次数

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摘要： Love’s first approximation theory is used to analyze the natural frequencies of rotating functionally graded cylindrical shells. To verify the validity of the present method, the natural frequencies of the simply supported non-rotating isotropic cylindrical shell and the functionally graded cylindrical shell are compared with available published results. Good agreement is obtained. The effects of the power law index, the wave numbers along the x- and θ-directions, and the thickness-to-radius ratio on the natural frequencies of the simply supported rotating functionally graded cylindrical shell are investigated by several numerical examples. It is found that the fundamental frequencies of the backward waves increase with the increasing rotating speed, the fundamental frequencies of the forward waves decrease with the increasing rotating speed, and the forward and backward waves frequencies increase with the increasing thickness-to-radius ratio.

Abstract: Love’s first approximation theory is used to analyze the natural frequencies of rotating functionally graded cylindrical shells. To verify the validity of the present method, the natural frequencies of the simply supported non-rotating isotropic cylindrical shell and the functionally graded cylindrical shell are compared with available published results. Good agreement is obtained. The effects of the power law index, the wave numbers along the x- and θ-directions, and the thickness-to-radius ratio on the natural frequencies of the simply supported rotating functionally graded cylindrical shell are investigated by several numerical examples. It is found that the fundamental frequencies of the backward waves increase with the increasing rotating speed, the fundamental frequencies of the forward waves decrease with the increasing rotating speed, and the forward and backward waves frequencies increase with the increasing thickness-to-radius ratio.

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