Acta Mechanica Sinica

, Volume 29, Issue 4, pp 593–601 | Cite as

Single-pulse chaotic dynamics of functionally graded materials plate

  • Yu-Gao HuangfuEmail author
  • Fang-Qi Chen
Research Paper


Single-pulse chaos are studied for a functionally graded materials rectangular plate. By means of the global perturbation method, explicit conditions for the existence of a Silnikov-type homoclinic orbit are obtained for this system, which suggests that chaos are likely to take place. Then, numerical simulations are given to test the analytical predictions. And from our analysis, when the chaotic motion occurs, there are a quasi-period motion in a two-dimensional subspace and chaos in another two-dimensional supplementary subspace.


Functionally graded materials Single-pulse Melnikov’s method Homoclinic orbit Numerical simulation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Koizumi, M.: The concept of FGM, ceramic transactions. Functionally Gradient Materials 34, 3–10 (1993)Google Scholar
  2. 2.
    Suresh, S., Mortensen, A.: Fundamentals of Functionally Graded Materials. The University Press, Cambridge (1998)Google Scholar
  3. 3.
    Jedrysiak, J., Radzikowska, A.: Tolerance averaging of heat conduction in transversally graded laminates. Meccanica 47, 95–107 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Yan, T., Yang, J., Kitipornchai, S.: Non-linear dynamic response of an edge-cracked functionally graded Timoshenko beam under parametric exicitation. Non-linear Dyn. 67, 527–540 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Jia, X.L., Yang, J., Kitipornchai, S., et al.: Free vibration of geometrically non-linear micro-switches under electrostatic and Casimir forces. Smart Materials and Structures 19, 1–13 (2010)CrossRefGoogle Scholar
  6. 6.
    Ke, L.L., Yang, J., Kitipornchai, S.: An analytical study on the non-linear vibration of functionally graded beams. Meccanica 45, 743–752 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Hao, Y.X., Chen, L.H., Zhang, W., et al.: Non-linear oscillations, bifurcations and chaos of functionally graded materials plate. Journal of Sound and Vibration 312, 862–892 (2008)CrossRefGoogle Scholar
  8. 8.
    Zhang, W., Yang, J., Hao, Y.X.: Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory. Non-linear Dyn. 59, 619–660 (2010)zbMATHCrossRefGoogle Scholar
  9. 9.
    Wiggins, S.: Global Bifurcations and Chaos. Springer, New York (1988)zbMATHCrossRefGoogle Scholar
  10. 10.
    Kovačič, G., Wiggins, S.: Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation. Physica D 57, 185–225 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Feng, Z.C., Wiggins, S.: On the existence of chaos in a class of two-degree-of-freedom, damped parametrically forced mechanical systems with broken O(2) symmetry. ZAMP 44, 201–248 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Feng, Z.C., Sethna, P.R.: Global bifurcation in motions of parametricaliy excited thin plates. Non-linear Dyn. 4, 398–408 (1993)CrossRefGoogle Scholar
  13. 13.
    Feng, Z.C., Liew, K.M.: Global bifurcations in parametrically excited systems with zero-to-one internal resonance. Nonlinear Dyn. 21, 249–263 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    McDonald, R.J., Namachchivaya, N. Sri: Pipes conveying pulsating fluid near a 0:1 resonance: Global bifurcations, Journal of Fluids and Structures 21, 665–687 (2005)CrossRefGoogle Scholar
  15. 15.
    Yeo, M.H., Lee, W.K.: Evidences of global bifurcations of an imperfect circular plate. Journal of Sound and Vibration 293, 138–155 (2006)CrossRefGoogle Scholar
  16. 16.
    Zhang, W., Wang, F.X., Yao, M.H.: Global bifurcations and chaotic dynamics in non-linear nonplanar oscillations of a parametrically excited cantilever beam, Non-linear Dyn. 40, 251–279 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Zhang, W., Zu, J.W., Wang, F.X.: Global bifurcations and chaos for a rotor-active magnetic bearing system with timevarying stiffness. Chaos, Solitons and Fractals 35, 586–608 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Cao, D.X., Zhang, W.: Global bifurcations and chaotic dynamics for a string-beam coupled system. Chaos, Solitons and Fractals 37, 858–875 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Yu, W.Q., Chen, F.Q.: Global bifurcations of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation. Non-linear Dyn. 59, 129–141 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Li, S.B., Zhang, W., Yao, M.H.: Using energy-phase method to study global bifurcations and Shilnikov-type multipulse chaotic dynamics for a non-linear vibration absorber. International Journal of Bifurcation and Chaos 22, 1250001 (2012)CrossRefGoogle Scholar
  21. 21.
    Yao, M.H., Zhang, W., Zu, J.W.: Multi-pulse chaotic dynamics in non-planar motion of parametrically excited viscoelastic moving belt. Journal of Sound and Vibration 331, 2624–2653 (2012)CrossRefGoogle Scholar
  22. 22.
    Zhang, J.H., Zhang, W.: An extended high-dimensional Melnikov analysis for global and chaotic dynamics of a nonautonomous rectangular buckled thin plate. Science China: Physics, Mechanics and Astronomy 55, 1679–1690 (2012)CrossRefGoogle Scholar
  23. 23.
    Yao, M.H., Zhang, W., Yao, Z.G.: Multi-pulse orbits dynamics of composite laminated piezoelectric rectangular plate. Science China Technological Sciences 54, 2064–2079 (2011)zbMATHCrossRefGoogle Scholar
  24. 24.
    Zhang, W., Li, S.B.: Resonant chaotic motions of a buckled rectangular thin plate with parametrically and externally excitations. Non-linear Dynamics 62, 673–686 (2010)zbMATHCrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceHenan Polytechnic UniversityJiaozuoChina
  2. 2.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingChina

Personalised recommendations