Advertisement

Acta Mechanica Solida Sinica

, Volume 26, Issue 3, pp 277–291 | Cite as

Nonlinear Vibration Response and Bifurcation of Circular Cylindrical Shells under Traveling Concentrated Harmonic Excitation

  • Yanqing Wang
  • Li Liang
  • Xinghui Guo
  • Jian Li
  • Jing Liu
  • Panglun Liu
Article

Abstract

The nonlinear vibration of a cantilever cylindrical shell under a concentrated harmonic excitation moving in a concentric circular path is proposed. Nonlinearities due to large-amplitude shell motion are considered, with account taken of the effect of viscous structure damping. The system is discretized by Galerkin’s method. The method of averaging is developed to study the nonlinear traveling wave responses of the multi-degrees-of-freedom system. The bifurcation phenomenon of the model is investigated by means of the averaged system in detail. The results reveal the change process and nonlinear dynamic characteristics of the periodic solutions of averaged equations.

Key Words

circular cylindrical shell nonlinearity traveling wave method of averaging bifurcation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fulcher, L.P. and Davis, B.F., Theoretical and experimental study of the motion of the simple pendulum. American Journal of Physics, 1976, 44: 51–55.CrossRefGoogle Scholar
  2. 2.
    Zavodney, L.D. and Nayfeh, A.H., The non-linear response of a slender beam carrying a lumped mass to a principal parametric excitation: theory and experiment. International Journal of Non-linear Mechanics, 1989, 24: 105–125.CrossRefGoogle Scholar
  3. 3.
    Dooren, R.V., Combination tones of summed type in a non-linear damped vibratory system with two degrees-of-freedom. International Journal of Non-linear Mechanics, 1971, 6: 237–254.CrossRefGoogle Scholar
  4. 4.
    Gabale, A.P. and Sinha, S.C., A direct analysis of nonlinear systems with external periodic excitations via normal forms. Nonlinear Dynamics, 2009, 55: 79–93.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Sanders, J.A. and Verhulst, F., Averaging Methods in Nonlinear Dynamical Systems. New York: Springer-Verlag, 1985.CrossRefGoogle Scholar
  6. 6.
    Huang, C.C., Moving loads on elastic cylindrical shells. Journal of Sound and Vibration, 1976, 49: 215–220.CrossRefGoogle Scholar
  7. 7.
    Ng, T.Y., Lam, K.Y., Liew, K.M. and Reddy, J.N., Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading. International Journal of Solids and Structures, 2001, 38: 1295–1309.CrossRefGoogle Scholar
  8. 8.
    Liew, K.M., Hu, Y.G., Zhao, X. and Ng, T.Y., Dynamic stability analysis of composite laminated cylindrical shells via the mesh-free kp-Ritz method. Computer Methods in Applied Mechanics and Engineering, 2006, 196147–160.Google Scholar
  9. 9.
    Liew, K.M., Hu, Y.G., Ng, T.Y. and Zhao, X., Dynamic stability of rotating cylindrical shells subjected to periodic axial loads. International Journal of Solids and Structures, 2006, 43: 7553–7570.CrossRefGoogle Scholar
  10. 10.
    Pellicano, F., Dynamic stability and sensitivity to geometric imperfections of strongly compressed circular cylindrical shells under dynamic axial loads. Communications in Nonlinear Science and Numerical Simulation, 2009, 14: 3449–3462.CrossRefGoogle Scholar
  11. 11.
    Huang, Y.M. and Fuller, C.R., The effect of dynamic absorbers on the forced vibration of a cylindrical shell and its coupled interior sound field. Journal of Sound and Vibration, 1997, 200: 401–418.CrossRefGoogle Scholar
  12. 12.
    Amabili, M., A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach. Journal of Sound and Vibration, 2003, 264: 1091–1125.CrossRefGoogle Scholar
  13. 13.
    Jafari, A.A., Khalili, S.M.R. and Azarafza, R., Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads. Thin-Walled Structures, 2005, 43: 1763–1786.CrossRefGoogle Scholar
  14. 14.
    Pellicano, F. and Amabili, M., Dynamic instability and chaos of empty and fluid-filled circular cylindrical shells under periodic axial loads. Journal of Sound and Vibration, 2006, 293: 227–252.CrossRefGoogle Scholar
  15. 15.
    Wang, Y.Q., Guo, X.H., Li, Y.G. and Li, J., Nonlinear traveling wave vibration of a circular cylindrical shell subjected to a moving concentrated harmonic force. Journal of Sound and Vibration, 2010, 329: 338–352.CrossRefGoogle Scholar
  16. 16.
    Pellicano, F., Dynamic instability of a circular cylindrical shell carrying a top mass under base excitation: Experiments and theory. International Journal of Solids and Structures, 2011, 48: 408–427.CrossRefGoogle Scholar
  17. 17.
    Wang, Y.Q., Guo, X.H., Chang, H.H. and Li, H.Y., Nonlinear dynamic response of rotating circular cylindrical shells with precession of vibrating shape-Part II: Approximate analytical solution. International Journal of Mechanical Sciences, 2010, 52(9): 1208–1216.CrossRefGoogle Scholar
  18. 18.
    Wang, Y.Q., Guo, X.H., Chang, H.H. and Li, H.Y., Nonlinear dynamic response of rotating circular cylindrical shells with precession of vibrating shape—Part I: Numerical solution. International Journal of Mechanical Sciences. 2010, 52(9): 1217–1224.CrossRefGoogle Scholar
  19. 19.
    Wolfram, S., The Mathematica Book. Cambridge: Cambridge University Press, 1999.zbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2013

Authors and Affiliations

  • Yanqing Wang
    • 1
    • 2
  • Li Liang
    • 2
  • Xinghui Guo
    • 1
  • Jian Li
    • 1
  • Jing Liu
    • 3
  • Panglun Liu
    • 1
  1. 1.Institute of Applied MechanicsNortheastern UniversityShenyangChina
  2. 2.School of Resources & Civil EngineeringNortheastern UniversityShenyangChina
  3. 3.Department of Automotive EngineeringJining PolytechnicJiningChina

Personalised recommendations