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Natural frequencies of rotating functionally graded cylindrical shells

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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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References

  1. Li, S. R., Fu, X. H., and Batra, R. C. Free vibration of three-layer circular cylindrical shells with functionally graded middle layer. Mechanics Research Communications, 37(3), 577–580 (2010)

    Article  Google Scholar 

  2. Sepiani, H. A., Rastgoo, A., Ebrahimi, F., and Arani, A. G. Vibration and buckling analysis of two-layered functionally graded cylindrical shell, considering the effects of transverse shear and rotary inertia. Materials and Design, 31(3), 1063–1069 (2010)

    Article  Google Scholar 

  3. Matsunaga, H. Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory. Composite Structures, 88(1), 519–531 (2009)

    Article  Google Scholar 

  4. Pradhan, S. C., Loy, C. T., Lam, K. Y., and Reddy, J. N. Vibration characteristics of functionally graded cylindrical shells under various boundary conditions. Applied Acoustics, 61(1), 111–129 (2000)

    Article  Google Scholar 

  5. Vel, S. S. Exact elasticity solution for the vibration of functionally graded anisotropic cylindrical shells. Composite Structures, 92(8), 2712–2727 (2010)

    Article  Google Scholar 

  6. Zhao, X., Liew, K. M., and Ng, T. Y. Vibrations of rotating cross-ply laminated circular cylindrical shells with stringer and ring stiffeners. International Journal of Solids and Structures, 39(2), 529–545 (2002)

    Article  MATH  Google Scholar 

  7. Civalek, Ö. and Gürses, M. Free vibration analysis of rotating cylindrical shells using discrete singular convolution technique. International Journal of Pressure Vessels and Piping, 86(7), 677–683 (2009)

    Article  Google Scholar 

  8. Liew, K. M., Ng, T. Y., Zhao, X., and Reddy, J. N. Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells. Computer Methods in Applied Mechanics and Engineering, 191(37–38), 4141–4157 (2002)

    Article  MATH  Google Scholar 

  9. Civalek, Ö. A parametric study of the free vibration analysis of rotating laminated cylindrical shells. Thin-Walled Structures, 45(7–8), 692–698 (2007)

    Article  Google Scholar 

  10. Hua, L. and Lam, K. Y. Frequency characteristics of a thin rotating cylindrical shell using the generalized differential quadrature method. International Journal of Mechanical Sciences, 40(2), 443–459 (1998)

    Article  MATH  Google Scholar 

  11. Zhang, X. M. Parametric analysis of frequency of rotating laminated composite cylindrical shells with the wave propagation approach. Computer Methods in Applied Mechanics and Engineering, 191(19–20), 2057–2071 (2002)

    Article  MATH  Google Scholar 

  12. Lam, K. Y. and Loy, C. T. On vibrations of thin rotating laminated composite cylindrical shells. Composites Engineering, 4(8), 1153–1167 (1994)

    Article  Google Scholar 

  13. Lam, K. Y. and Loy, C. T. Free vibrations of a rotating multilayered cylindrical shell. International Journal of Solids and Structures, 32(5), 647–663 (1995)

    Article  MATH  Google Scholar 

  14. Warburton, G. B. Vibration of thin cylindrical shells. Journal of Mechanical Engineering Science, 7, 399–407 (1965)

    Article  Google Scholar 

  15. Loy, C. T., Lam, K. Y., and Reddy, J. N. Vibration of functionally graded cylindrical shells. International Journal of Mechanical Sciences, 41(3), 309–324 (1999)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Liaoning Key Laboratory of General Aviation, Shenyang Aerospace University, Shenyang, 110136, P. R. China

    Song Xiang  (项 松)

  2. Liaoning General Aviation Academy, Shenyang, 110136, P. R. China

    Song Xiang  (项 松)

  3. School of Power and Energy Engineering, Shenyang Aerospace University, Shenyang, 110136, P. R. China

    Guang-chao Li  (李广超), Wei Zhang  (张 魏) & Ming-sui Yang  (杨明绥)

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  1. Song Xiang  (项 松)
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  2. Guang-chao Li  (李广超)
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  3. Wei Zhang  (张 魏)
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  4. Ming-sui Yang  (杨明绥)
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Correspondence to Song Xiang  (项 松).

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Xiang, S., Li, Gc., Zhang, W. et al. Natural frequencies of rotating functionally graded cylindrical shells. Appl. Math. Mech.-Engl. Ed. 33, 345–356 (2012). https://doi.org/10.1007/s10483-012-1554-6

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  • DOI: https://doi.org/10.1007/s10483-012-1554-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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