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Journal of Vibration Engineering & Technologies

, Volume 6, Issue 6, pp 453–469 | Cite as

Nonlinear Vibrations of FGM Circular Conical Panel Under In-Plane and Transverse Excitation

  • Y. X. Hao
  • Y. Niu
  • W. ZhangEmail author
  • M. H. Yao
  • S. B. Li
Original Paper

Abstract

Purpose

In this study, nonlinear forced vibrations of a functionally graded material circular conical panel under the transverse excitation and the in-plane excitation are discussed.

Method

The temperature field of the system is considered as a steady-state temperature. Material properties of temperature-dependence for the system vary along the thickness direction in the light of a power law. The nonlinear geometric partial differential equations expressed by general displacements are derived by the first-order shear deformation theory and Hamilton’s principle. Furthermore, the ordinary differential equations of the system are acquired by the Galerkin method. The nonlinear dynamic behaviors of the system are fully analyzed.

Results

Based on numerical simulations, time history records, Poincare maps, phase portraits and bifurcation diagrams are depicted to clarify the existence of complex nonlinear dynamic behaviors of the system.

Keywords

Functionally graded material Circular conical panel Nonlinear dynamics Chaotic motion 

Notes

Acknowledgements

This paper is fully supported by National Natural Science Foundation of China (11272063, 11472056 and 11290152) and Natural Science Foundation of Tianjin City (13JCQNJC04400).

References

  1. 1.
    Sofiyev AH, Kuruoglu N (2015) On a problem of the vibration of functionally graded conical shells with mixed boundary conditions. Compos B 70:122–130CrossRefGoogle Scholar
  2. 2.
    Sofiyev AH (2009) The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure. Compos Struct 89:356–366CrossRefGoogle Scholar
  3. 3.
    Teichmann D (1985) An approximation of the lowest eigen frequencies and buckling loads of cylindrical and conical shell panels under initial stress. AIAA J 23:1634–1637CrossRefGoogle Scholar
  4. 4.
    Qiu WB, Zhou ZH, Xu XS (2016) The dynamic behavior of circular plates under impact loads. J Vib Eng Technol 4:111–116Google Scholar
  5. 5.
    Srinivasan RS, Krishnan PA (1987) Free vibration of conical shell panels. J Sound Vib 117:153–160CrossRefGoogle Scholar
  6. 6.
    Lim CW, Liew KM (1995) Vibratory behaviour of shallow conical shells by a global Ritz formulation. Eng Struct 17:63–69CrossRefGoogle Scholar
  7. 7.
    Lim CW, Liew KM, Kitipornchai S (1998) Vibration of cantilevered laminated composite shallow conical shells. Int J Solids Struct 35:1695–1707CrossRefGoogle Scholar
  8. 8.
    Lim CW, Liew KM (1996) Vibration of shallow conical shells with shear flexibility: a first-order theory. Int J Solids Struct 33:451–468CrossRefGoogle Scholar
  9. 9.
    Lim CW, Kitipornchai S (1999) Effects of subtended and vertex angles on the free vibration of open conical shell panels: a conical coordinate approach. J Sound Vib 219:813–835CrossRefGoogle Scholar
  10. 10.
    Lam KY, Li H, Ng TY, Chua CF (2002) Generalized differential quadrature method for the free vibration of truncated conical panels. Journal of Sound and Vibration 251:329–348CrossRefGoogle Scholar
  11. 11.
    Pinto Correia IF, Mota Soares CM, Mota Soares CA, Herskovits J (2003) Analysis of laminated conical shell structures using higher order models. Compos Struct 62:383–390CrossRefGoogle Scholar
  12. 12.
    Dey S, Karmakar A (2012) Free vibration analyses of multiple delaminated angle-ply composite conical shells—a finite element approach. Compos Struct 94:2188–2196CrossRefGoogle Scholar
  13. 13.
    Zhao X, Li Q, Liew KM, Ng TY (2006) The element-free kp-Ritz method for free vibration analysis of conical shell panels. J Sound Vib 295:906–922CrossRefGoogle Scholar
  14. 14.
    Sofiyev AH (2004) The stability of functionally graded truncated conical shells subjected to aperiod impulsive loading. Int J Solids Struct 41:3411–3424CrossRefGoogle Scholar
  15. 15.
    Naj R, Sabzikar Boroujerdy M, Eslami MR (2008) Thermal and mechanical instability of functionally graded truncated conical shells. Thin Walled Struct 46:65–78CrossRefGoogle Scholar
  16. 16.
    Zhang JH, Li SR (2010) Dynamic buckling of FGM truncated conical shells subjected to non-uniform normal impact load. Compos Struct 92:2979–2983CrossRefGoogle Scholar
  17. 17.
    Sofiyev AH (2012) The non-linear vibration of FGM truncated conical shells. Compos Struct 94:2237–2245CrossRefGoogle Scholar
  18. 18.
    Sofiyev AH, Kuruoglu N (2013) Effect of a functionally graded interlayer on the non-linear stability of conical shells in elastic medium. Compos Struct 99:296–308CrossRefGoogle Scholar
  19. 19.
    Deniz A (2013) Non-linear stability analysis of truncated conical shell with functionally graded composite coatings in the finite deflection. Compos B 51:318–326CrossRefGoogle Scholar
  20. 20.
    Duc ND, Cong PH (2015) Nonlinear thermal stability of eccentrically stiffened functionally graded truncated conical shells surrounded on elastic foundations. Eur J Mech A Solids 50:120–131MathSciNetCrossRefGoogle Scholar
  21. 21.
    Zhao X, Liew KM (2011) Free vibration analysis of functionally graded conical shell panels by a meshless method. Compos Struct 93:649–664CrossRefGoogle Scholar
  22. 22.
    Akbari M, Kiani Y, Aghdam MM, Eslami MR (2014) Free vibration of FGM Lévy conical panels. Compos Struct 116:732–746CrossRefGoogle Scholar
  23. 23.
    Bich DH, Phuong NT, Tung HV (2012) Buckling of functionally graded conical panels under mechanics loads. Compos Struct 94:1379–1384CrossRefGoogle Scholar
  24. 24.
    Nosir A, Reddy JN (1991) A study of non-linear dynamic equations of higher-order deformation plate theories. Int J Non Linear Mech 26:233–249CrossRefGoogle Scholar
  25. 25.
    Bhimaraddi A (1999) Large amplitude vibrations of imperfect antisymmetric angle-ply laminated plates. J Sound Vib 162:457–470CrossRefGoogle Scholar
  26. 26.
    Reddy JN (2004) Mechanics of laminated composite plates and shells: theory and analysis. CRC Press, New YorkCrossRefGoogle Scholar
  27. 27.
    Shen HS (2009) Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium. Int J Mech Sci 51:372–383CrossRefGoogle Scholar

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Authors and Affiliations

  • Y. X. Hao
    • 1
  • Y. Niu
    • 2
  • W. Zhang
    • 2
    Email author
  • M. H. Yao
    • 2
  • S. B. Li
    • 3
  1. 1.College of Mechanical EngineeringBeijing Information Science and Technology UniversityBeijingPeople’s Republic of China
  2. 2.College of Mechanical EngineeringBeijing University of TechnologyBeijingPeople’s Republic of China
  3. 3.College of ScienceCivil Aviation University of ChinaTianjinPeople’s Republic of China

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