Skip to main content
SpringerLink
Log in

Nonlinear dynamics analysis of a two-dimensional thin panel with an external forcing in incompressible subsonic flow

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

Abstract

Based on the potential theory of incompressible flow and the energy method, a two-dimensional simply supported thin panel subjected to external forcing and uniform incompressible subsonic flow is theoretically modeled. The nonlinear cubic stiffness and viscous damper in the middle of the panel is considered. Transformation of the governing partial differential equation to a set of ordinary differential equations is performed through the Galerkin method. The stability of the fixed points of the panel system is analyzed. The regions of different motion types of the panel system are investigated in different parameter spaces. The rich dynamic behaviors are presented as bifurcation diagrams, phase-plane portraits, Poincaré maps and maximum Lyapunov exponents based on carefully numerical simulations.

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. Schetz, J.A.: Aerodynamics of high-speed trains. Annu. Rev. Fluid Mech. 33, 371–414 (2001)

    Article  Google Scholar 

  2. Jeromr, C.R.: A train for the 21st century. Rail Int., 2–8 (1994)

  3. Raghunathan, R.S., Kim, H.D., Setoguchi, T.: Aerodynamics of high-speed railway trains. Prog. Aerosp. Sci. 38, 469–514 (2002)

    Article  Google Scholar 

  4. Dowell, E.H.: Flutter of a buckled plate as an example of chaotic motion of a deterministic autonomous system. J. Sound Vib. 85, 333–344 (1982)

    Article  MathSciNet  Google Scholar 

  5. Kobayashi, S.: Flutter of a simply supported rectangular panels in a supersonic flow-two dimensional panel flutter, I simply supported, II clamped panels. Trans. Jpn. Soc. Aeron. Space Sci. 5, 79–119 (1962)

    Google Scholar 

  6. Koo, K.N., Hwang, W.S.: Effects of hysteretic and aerodynamic damping on supersonic panel flutter of composite plates. J. Sound Vib. 273, 569–583 (2004)

    Article  Google Scholar 

  7. Yuen, S.W., Lau, S.L.: Effects of inplane load on nonlinear panel flutter by incremental harmonic balance method. AIAA J. 29, 1472–1479 (1991)

    Article  Google Scholar 

  8. Chen, D.L., Yang, Y.R., Fan, C.G.: Nonlinear flutter of a two-dimension thin plate subjected to aerodynamic heating by differential quadrature method. Acta Mech. Sin. 24, 45–50 (2008)

    Article  Google Scholar 

  9. Dugundji, J., Dowell, E.H., Perkin, B.: Subsonic flutter of panels on continuous elastic foundations. AIAA J. 1, 1146–1154 (1963)

    Article  Google Scholar 

  10. Kornecki, A.: Static and dynamic instability of panels and cylindrical shells in subsonic potential flow. J. Sound Vib. 32, 251–263 (1974)

    Article  MATH  Google Scholar 

  11. Kornecki, A., Dowell, E.H., O’Brien, J.: On the aeroelastic instability of two-dimensional panels in unform incompressible flow. J. Sound Vib. 47, 163–178 (1974)

    Article  Google Scholar 

  12. Guo, C.Q., Paidoussis, M.P.: Stability of rectangular plates with free side-edges in two-dimensional inviscid channel flow. J. Appl. Mech. 67, 171–176 (2000)

    Article  MATH  Google Scholar 

  13. Awrejcewicz, J., Krysko, V.A., Narkaitis, G.G.: Bifurcations of a thin plate-strip excited transversally and axially. Nonlinear Dyn. 32, 187–209 (2003)

    Article  MATH  Google Scholar 

  14. Akour, S.N., Nayfeh, J.F.: Nonlinear dynamics of polar-orthotropic circular plates. Int. J. Struct. Stab. Dyn. 6, 253–268 (2006)

    Article  Google Scholar 

  15. Wang, L., Ni, Q., Huang, Y.Y.: Bifurcations and chaos in forced cantilever system with impacts. J. Sound Vib. 296, 1068–1078 (2006)

    Article  Google Scholar 

  16. Jing, Z.J., Wang, R.Q.: Complex dynamic in Duffing system with two external forcings. Chaos Solitons Fractals 25, 399–411 (2005)

    Article  MathSciNet  Google Scholar 

  17. Huang, J.C., Jing, Z.J.: Bifurcations and chaos in three-well Duffing system with one external forcing. Chaos Solitons Fractals 40, 1449–1466 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kenfack, A.: Bifurcation structure of two coupled periodically driven double-well Duffing oscillators. Chaos Solitons Fractals 15, 205–218 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  19. Ye, M., Chen, Y.S.: Period doubling bifurcation in elastic bulked beam under parametric excitation. Acta Mech. Solida Sin. 19, 361–164 (1998)

    Google Scholar 

  20. Zhang, W., Huo, Q.Z.: Bifurcation of nonlinear oscillation system under combined parametric and forcing excitation. Acta Mech. Sin. 23, 464–474 (1991)

    MathSciNet  Google Scholar 

  21. Zhang, W., Liu, Z.M., Yu, P.: Global dynamic of a parametrically and externally excited thin plate. Nonlinear Dyn. 24, 245–268 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  22. Awrejcewicz, J.: Bifurcations and Chaos in Simple Dynamical Systems. World Scientific, Singapore (1989), 126 pp.

    Google Scholar 

  23. Awrejcewicz, J.: Bifurcations and Chaos in Coupled Oscillators. World Scientific, Singapore (1991), 245 pp.

    Google Scholar 

  24. Awrejcewicz, J., Krysko, V.A.: Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells. World Scientific, Berlin (2003), 428 pp.

    Book  MATH  Google Scholar 

  25. Bisplinghoff, R.L., Ashley, H., Halfman, R.L.: Aeroelasticity. Addison-Wesley, Cambridge (1955)

    MATH  Google Scholar 

  26. Dowell, E.H.: Aeroelasticity of Plates and Shells. Nordhoff, Leyden (1975)

    MATH  Google Scholar 

  27. Zhang, J.Y., Yang, Y.R., Zeng, J.: An algorithm criterion for Hopf bifurcation and its application in vehicle dynamic. Acta Mech. Sin. 32, 596–605 (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Traction Power Laboratory, Southwest Jiaotong University, Chengdu, 610031, P.R. China

    Peng Li

  2. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 610031, P.R. China

    Yiren Yang & Wei Xu

Authors
  1. Peng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yiren Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peng Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, P., Yang, Y. & Xu, W. Nonlinear dynamics analysis of a two-dimensional thin panel with an external forcing in incompressible subsonic flow. Nonlinear Dyn 67, 2483–2503 (2012). https://doi.org/10.1007/s11071-011-0162-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-011-0162-8

Keywords

Search

Navigation