Skip to main content
Log in

Bifurcation and Chaos of Piezoelectric Shell Reinforced with BNNTs Under Electro-Thermo-Mechanical Loadings

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

By employing the nonlinear von Kármán shell theory and the theory of piezoelectricity including thermal effects, the constitutive relations of the BNNT-reinforced piezoelectric shell are built. Recurring to the ‘XY’ rectangle model, the material constants are reckoned. Then, the nonlinear governing equations of the structure are derived through the Reissner variational principle and solved by the fourth-order Runge–Kutta method. In numerical calculations, the effects of temperature, voltage, volume fraction, etc., on the bifurcation and chaos of piezoelectric shell reinforced with BNNTs are discussed in detail.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. An F, Chen F. Bifurcations and chaos of the nonlinear viscoelastic plates subjected to subsonic flow and external loads. Chaos Solitons Fractals. 2016;91:78–85.

    Article  MathSciNet  MATH  Google Scholar 

  2. Yiming F, Wang J, Mao Y. Nonlinear analysis of buckling, free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment. Appl Math Model. 2012;36(9):4324–40.

    Article  MathSciNet  MATH  Google Scholar 

  3. Yiqi M, Yiming F. Nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate. J Sound Vib. 2010;329(11):2015–28.

    Article  Google Scholar 

  4. Selim BA, Zhang LW, Liew KM. Active vibration control of CNT-reinforced composite plates with piezoelectric layers based on Reddy’s higher-order shear deformation theory. Compos Struct. 2017;163:350–64.

    Article  Google Scholar 

  5. Fakhari V, Ohadi A, Yousefian P. Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment. Compos Struct. 2011;93(9):2310–21.

    Article  MATH  Google Scholar 

  6. Detroux T, Renson L, Masset L, Kerschen G. The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems. Comput Methods Appl Mech Eng. 2015;296:18–38.

    Article  MathSciNet  MATH  Google Scholar 

  7. Behjat B, Khoshravan MR. Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates. Compos Struct. 2012;94(3):874–82.

    Article  Google Scholar 

  8. Li C, Liu JJ, Cheng M, Fan XL. Nonlocal vibrations and stabilities in parametric resonance of axially moving viscoelastic piezoelectric nanoplate subjected to thermo-electro-mechanical forces. Compos B Eng. 2017;116:153–69.

    Article  Google Scholar 

  9. Larbi W, Deü J-F, Ohayon R. Finite element formulation of smart piezoelectric composite plates coupled with acoustic fluid. Compos Struct. 2012;94(2):501–9.

    Article  Google Scholar 

  10. Liu D, Yong X, Junlin L. Randomly-disordered-periodic-induced chaos in a piezoelectric vibration energy harvester system with fractional-order physical properties. J Sound Vib. 2017;399:182–96.

    Article  Google Scholar 

  11. Padmanav Dash BN, Singh BN. Nonlinear free vibration of piezoelectric laminated composite plate. Finite Elements Anal Des. 2009;45(10):686–94.

    Article  Google Scholar 

  12. Song ZG, Zhang LW, Liew KM. Active vibration control of CNT-reinforced composite cylindrical shells via piezoelectric patches. Compos Struct. 2016;158:92–100.

    Article  Google Scholar 

  13. Selim BA, Zhang LW, Liew KM. Active vibration control of FGM plates with piezoelectric layers based on Reddy’s higher-order shear deformation theory. Compos Struct. 2016;155(1):118–34.

    Article  Google Scholar 

  14. Zhang HY, Shen YP. Vibration suppression of laminated plates with 1–3 piezoelectric fiber-reinforced composite layers equipped with interdigitated electrodes. Compos Struct. 2007;79(2):220–8.

    Article  Google Scholar 

  15. Zhang LW, Song ZG, Qiao P, Liew KM. Modeling of dynamic responses of CNT-reinforced composite cylindrical shells under impact loads. Comput Methods Appl Mech Eng. 2017;313:889–903.

    Article  MathSciNet  Google Scholar 

  16. Krysko VA, Awrejcewicz J, Kutepov IE, Zagniboroda NA, Papkova IV, Serebryakov AV, Krysko AV. Chaotic dynamics of flexible beams with piezoelectric and temperature phenomena. Phys Lett A. 2013;377:2058–61.

    Article  MathSciNet  Google Scholar 

  17. Mohammadzadeh-Keleshteri M, Asadi H, Aghdam MM. Geometrical nonlinear free vibration responses of FG-CNT reinforced composite annular sector plates integrated with piezoelectric layers. Compos Struct. 2017;171:100–12.

    Article  Google Scholar 

  18. Saviz MR, Mohammadpourfard M. Dynamic analysis of a laminated cylindrical shell with piezoelectric layers under dynamic loads. Finite Elements Anal Des. 2010;46:770–81.

    Article  MathSciNet  Google Scholar 

  19. Rafiee M, Yang J, Kitipornchai S. Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers. Compos Struct. 2013;96:716–25.

    Article  Google Scholar 

  20. Ying ZG, Zhu XQ. Response analysis of piezoelectric shells in plane strain under random excitations. Acta Mechanica Solida Sinica. 2009;22:152–60.

    Article  Google Scholar 

  21. Rezaee M, Jahangiri R. Nonlinear and chaotic vibration and stability analysis of an aero- elastic piezoelectric FG plate under parametric and primary excitations. J Sound Vib. 2015;344(26):277–96.

    Article  Google Scholar 

  22. Mosallaie Barzoki AA, Ghorbanpour Arani A, Kolahchi R, Mozdianfard MR. Electro–thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core. Appl Math Model. 2012;36:2977–89.

    Article  MathSciNet  MATH  Google Scholar 

  23. Mosallaie Barzoki AA, Ghorbanpour Arani A, Kolahchi R, Mozdianfard MR, Loghman A. Nonlinear buckling response of embedded piezoelectric cylindrical shell reinforced with BNNT under electro–thermo- mechanical loadings using HDQM. Compos B Eng. 2013;44(1):722–7.

    Article  Google Scholar 

  24. Ghorbanpour Arani A, Amir S, Shajari AR, Mozdianfard MR. Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory. Compos B Eng. 2012;43:195–203.

    Article  Google Scholar 

  25. Mercan K, Civalek Ö. DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix. Compos Struct. 2016;143(20):300–9.

    Article  Google Scholar 

  26. Ghorbanpour Arani A, Shajari AR, Amir S, Loghman A. Electro-thermo-mechanical nonlinear nonlocal vibration and instability of embedded micro-tube reinforced by BNNT conveying fluid. Phys E Low-dimens Syst Nanostruct. 2012;45:109–21.

    Article  Google Scholar 

  27. Ghorbanpour Arani A, Shajari AR, Atabakhshian V, Amir S, Loghman A. Nonlinear dynamical response of embedded fluid-conveyed micro-tube reinforced by BNNTs. Compos B Eng. 2013;44(1):424–32.

    Article  Google Scholar 

  28. Ghorbanpour Arani A, Roudbari MA, Amir S. Nonlocal vibration of SWBNNT embedded in bundle of CNTs under a moving nanoparticle. Phys B Condens Matter. 2012;407(17):3646–53.

    Article  Google Scholar 

  29. Ansari R, Norouzzadeh A, Gholami R, Faghih M, Shojaei M, Hosseinzadeh M. Size-dependent nonlinear vibration and instability of embedded fluid-conveying SWBNNTs in thermal environment. Phys E Low-dimens Syst Nanostruct. 2014;61:148–57.

    Article  Google Scholar 

  30. Yang JH, Yang J, Kitipornchai S. Nonlinear dynamic response of electro-thermo- mechanically loaded piezoelectric cylindrical shell reinforced with BNNTs. Smart Mater Struct. 2012;21(12):1–11.

    Google Scholar 

  31. Sai N, Mele EJ. Microscopic theory for nanotube piezoelectricity. Phys Rev B. 2003;68:1405.

    Article  Google Scholar 

  32. Tan P, Tong L. Micro-electromechanics models for piezoelectric-fiber-reinforced composite materials. Compos Sci Technol. 2001;61:759–69.

    Article  Google Scholar 

  33. Fu YM. Nonlinear dynamic analysis of structures. Guang Zhou: Jinan University Press; 1997 (in Chinese).

    Google Scholar 

  34. Fu YM, Wang XQ. Analysis of bifurcation and chaos of the piezoelectric plate including damage effects. Int J Nonlinear Sci Numer Simul. 2008;9(1):61–74.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors wish to acknowledge with great appreciation for the supports from National Natural Science Foundation of China (Project No. 51822803).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jinhua Yang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, J., Zhou, T. Bifurcation and Chaos of Piezoelectric Shell Reinforced with BNNTs Under Electro-Thermo-Mechanical Loadings. Acta Mech. Solida Sin. 32, 120–132 (2019). https://doi.org/10.1007/s10338-018-0062-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10338-018-0062-2

Keywords

Navigation