Skip to main content
SpringerLink
Log in

Nonlinear vibrations of rotating thin circular cylindrical shell

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Nonlinear vibrations of thin circular cylindrical shells are investigated in this paper. Based on Love thin shell theory, the governing partial differential equations of motion for the rotating circular cylindrical shell are formulated using Hamilton principle. Taking into account the clamped-free boundary conditions, the partial differential system is truncated by using the Galerkin method. Sequentially, the effects of temperature, geometric parameters, circumferential wave number, axial half wave number and rotating speed on the nature frequency of the rotating circular cylindrical shell are studied. The dynamic responses of the rotating circular cylindrical shell are also investigated in time domain and frequency domain. Then, the effects of nonlinearity, excitation and damping on frequency responses of steady solution are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Amabili, M., Paidoussis, M.P.: Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Appl. Mech. Rev. 56(4), 349–381 (2003)

    Article  Google Scholar 

  2. Goncalves, P.B., Silva, F.M.A., DelPrado, Z.J.G.N.: Transient and steady state stability of cylindrical shells under harmonic axial loads. Int. J. Non-Linear Mech. 42, 58–70 (2007)

    Article  MATH  Google Scholar 

  3. Pellicano, F., Amabili, M., Paidoussis, M.P.: Effect of the geometry on the non-linear vibration of circular cylindrical shells. Int. J. Non-Linear Mech. 37, 1181–1198 (2002)

    Article  MATH  Google Scholar 

  4. Rougui, M., Moussaoui, F., Benamar, R.: Geometrically non-linear free and forced vibrations of simply supported circular cylindrical shells: A semi-analytical approach. Int. J. Non-Linear Mech. 42, 1102–1115 (2007)

    Article  MATH  Google Scholar 

  5. Amabili, M.: A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach. J. Sound Vib. 264, 1091–1125 (2003)

    Article  Google Scholar 

  6. Bryan, G.H.: On the beats in the vibration of revolving cylinder or bell. Math. Proc. Camb. Philos. Soc. 7, 101–111 (1890)

    Google Scholar 

  7. Lam, K.Y., Loy, C.T.: Analysis of rotating laminated cylindrical shells by different thin shell theories. J. Sound Vib. 186(1), 23–35 (1995)

    Article  MATH  Google Scholar 

  8. Loy, C.T., Lam, K.Y.: Vibration of rotating thin cylindrical panels. Appl. Acoust. 46, 327–343 (1995)

    Article  Google Scholar 

  9. Lam, K.Y., Loy, C.T.: Free vibrations of a rotating multi-layered cylindrical shell. Int. J. Solids Struct. 32(5), 647–663 (1995)

    Article  MATH  Google Scholar 

  10. Rand, O., Stavsky, Y.: Response and eigenfrequencies of rotating composite cylindrical shells. J. Sound Vib. 193(1), 65–77 (1996)

    Article  Google Scholar 

  11. Lam, K.Y., Loy, C.T.: On vibrations of thin rotating laminated composite cylindrical shells. Compos. Eng. 4(11), 1153–1167 (1994)

    Article  Google Scholar 

  12. Zhang, X.M.: Parametric analysis of frequency of rotating laminated composite cylindrical shells with the wave propagation approach. Comput. Methods Appl. Mech. Eng. 191, 2029–2043 (2002)

    Google Scholar 

  13. Lee, Y.S., Kim, Y.W.: Nonlinear free vibration analysis of rotating hybrid cylindrical shells. Comput. Struct. 70, 161–168 (1999)

    Article  MATH  Google Scholar 

  14. Huang, S.C., Hsu, B.S.: Resonant phenomena of a rotating cylindrical shell subjected to a harmonic moving load. J. Sound Vib. 136, 215–228 (1990)

    Article  Google Scholar 

  15. Ng, T.Y., Lam, K.Y.: Vibration and critical speed of a rotating cylindrical shell subjected to axial loading. Appl. Acoust. 56, 273–282 (1999)

    Article  Google Scholar 

  16. Ng, T.Y., Lam, K.Y., Reddy, J.N.: Parametric resonance of a rotating cylindrical shell subjected to periodic axial loads. J. Sound Vib. 214, 513–529 (1998)

    Article  Google Scholar 

  17. Pellicano, F., Amabili, M.: Stability and vibration of empty and fluid-filled circular cylindrical shells under static and periodic axial loads. Int. J. Solids Struct. 40, 3229–3251 (2003)

    Article  MATH  Google Scholar 

  18. Avramov, K.V., Mikhlin, Y.V., Kurilov, E.: Asymptotic analysis of nonlinear dynamics of simply supported cylindrical shells. Nonlinear Dyn. 47, 331–352 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  19. Swamy Naidu, N.V., Sinha, P.K.: Nonlinear free vibration analysis of laminated composite shells in hygrothermal environments. Compos. Struct. 77, 475–483 (2007)

    Article  Google Scholar 

  20. Amabili, M., Reddy, J.N.: A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells. Int. J. Non-Linear Mech. 45, 409–418 (2010)

    Article  Google Scholar 

  21. Li, X.B.: Study on free vibration analysis of circular cylindrical shells using wave propagation. J. Sound Vib. 311, 667–682 (2008)

    Article  Google Scholar 

  22. Lam, K.Y., Loy, C.T.: Influence of boundary conditions for a thin laminated rotating cylindrical shell. Compos. Struct. 41, 215–228 (1998)

    Article  Google Scholar 

  23. Lee, Y.S., Kim, Y.W.: Effect of boundary conditions on natural frequencies for rotating composite cylindrical shells with orthogonal stiffeners. Adv. Eng. Softw. 30, 649–655 (1999)

    Article  Google Scholar 

  24. Zhang, X.M.: Vibration analysis of cross-ply laminated composite cylindrical shells using the wave propagation approach. Appl. Acoust. 62, 1221–1228 (2001)

    Article  Google Scholar 

  25. Jafari, A.A., Khalili, S.M.R., Azarafza, R.: Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads. Thin-Walled Struct. 43, 1763–1786 (2005)

    Article  Google Scholar 

  26. Jansen, E.L.: Effect of boundary conditions on nonlinear vibration and flutter of laminated cylindrical shells. J. Vib. Acoust. 130, 1–8 (2008)

    Article  MathSciNet  Google Scholar 

  27. Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity, 4th edn. Cambridge University Press, Cambridge (1952)

    Google Scholar 

  28. Amabili, M., Pellicano, F., Paidoussis, M.P.: Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid, part II: large-amplitude vibrations without flow. J. Sound Vib. 228(5), 1103–1124 (1999)

    Article  Google Scholar 

  29. Wang, Y.Q., Guo, X.H., Li, Y.G., Li, J.: Nonlinear traveling wave vibration of a circular cylindrical shell subjected to a moving concentrated harmonic force. J. Sound Vib. 329, 338–392 (2010)

    Article  Google Scholar 

  30. Lam, K.Y., Loy, C.T.: Influence of boundary conditions and fibre orientation on the natural frequencies of thin orthotropic laminated cylindrical shells. Compos. Struct. 31(1), 21–30 (1995)

    Article  Google Scholar 

  31. Bhimaraddi, A.: Large amplitude vibrations of imperfect antisymmetric angle-ply laminated plates. J. Sound Vib. 162, 457–470 (1999)

    Article  Google Scholar 

  32. Nosir, A., Reddy, J.N.: A study of non-linear dynamic equations of higher-order deformation plate theories. Int. J. Non-Linear Mech. 26, 233–249 (1991)

    Article  Google Scholar 

  33. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, 100084, China

    Yanqi Liu & Fulei Chu

Authors
  1. Yanqi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fulei Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fulei Chu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, Y., Chu, F. Nonlinear vibrations of rotating thin circular cylindrical shell. Nonlinear Dyn 67, 1467–1479 (2012). https://doi.org/10.1007/s11071-011-0082-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-011-0082-7

Keywords

Search

Navigation