Skip to main content

Advertisement

SpringerLink
Log in

Multi-pulse jumping orbits and chaos of a fluid-conveying functionally graded cylindrical shell under piezoelectric and parametric excitations

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Abstract

The multi-pulse orbits and global dynamics of a fluid-conveying functionally graded cylindrical shell with piezoelectric layer are investigated by applying the energy-phase method. In the case of 1:2 internal resonance and 1/2 subharmonic resonance, the averaged equations for amplitudes and phases of thermal modes are considered. Some coordinate transformations are used to obtain the near-integrable standard forms. The energy-phase method is applied to prove the existence of Shilnikov-type multi-pulse jumping orbits homoclinic to a slow manifold in the perturbed phase space. The pulse sequences and homoclinic trees that depict the repeated bifurcations of the multi-pulse solutions are exhibited for both the Hamilton and dissipative perturbation. The results show that the pulse numbers start to decrease and the homoclinic trees gradually break up as the dissipation factor is increased. The research may reveal the mechanism how energy flow between high-frequency mode and low-frequency mode. Numerical simulations are also performed to discuss the influence of fluid damping, structure damping, and external excitation parameters on chaotic behaviors for the cylindrical shell.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Paak M, Paidoussis MP, Misra AK (2014) Influence of steady viscous forces on the non-linear behaviour of cantilevered circular cylindrical shells conveying fluid. Int J Nonlinear Mech 58:167–183

    Article  Google Scholar 

  2. Nurul Lzyan MD, Aziz ZA, Rabih Ghostine, Lee JH, Viswanathan KK (2019) Free vibration of cross-ply layered circular cylindrical shells filled with quiescent fluid under first order shear deformation theory. Int J Press Vessel Piping 170:73–81

    Article  Google Scholar 

  3. Chehreghani M, Pazhooh MD, Shakeri M (2019) Vibration analysis of a fluid conveying sandwich cylindrical shell with a soft core. Compos Struct 230:111470

    Article  Google Scholar 

  4. Lakis A, Laveau A (1991) Non-linear dynamic analysis of anisotropic cylindrical shells containing a flowing fluid. Int J Solids Struct 28:1079–1094

    Article  MATH  Google Scholar 

  5. Amabili M, Pellicano F, Paidoussis MP (2000) Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part III: truncation effect without flow and experiments. J Sound Vib 237:617–640

    Article  Google Scholar 

  6. Amabili M, Pellicano F, Paidoussis MP (2000) Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part IV: large amplitude vibrations with flow. J Sound Vib 237:641–666

    Article  Google Scholar 

  7. PaaK M, Paidoussis MP, Misra AK (2013) Nonlinear dynamics and stability of cantilevered circular cylindrical shells conveying fluid. J Sound Vib 322:3474–3498

    Article  Google Scholar 

  8. Tubaldi E, Amabili M, Paidoussis MP (2016) Fluid-structure interaction for nonlinear response of shells conveying pulsatile flow. J Sound Vib 371:252–276

    Article  Google Scholar 

  9. Sheng GG, Wang X (2017) Nonlinear response of fluid-conveying functionally graded cylindrical shells subjected to mechanical and thermal loading conditions. Compos Struct 168:675–684

    Article  Google Scholar 

  10. Zhang YF, Liu T, Zhang W (2020) Nonlinear resonant responses, mode interactions, and multitime periodic and chaotic oscillations of a cantilevered pipe conveying pulsating fluid under external harmonic force. Complexity 9840860

  11. Rafiee M, Mohammadi M, Sobhani Aragh B, Yaghoobi H (2013) Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells, Part I: theory and analytical solutions. Compos Struct 103:179–187

    Article  Google Scholar 

  12. Ninh DG, Tien ND (2019) Investigation for electro-thermo-mechanical vibration of nanocomposite cylindrical shells with an internal fluid flow. Aerosp Sci Technol 92:501–519

    Article  Google Scholar 

  13. Wang D, Chang QB, Zhang HY (2020) Nonlinear vibrations of fluid-conveying FG cylindrical shells with piezoelectric actuator layer and subjected to external and piezoelectric parametric excitations. Compos Struct 248:112437

    Article  Google Scholar 

  14. Melnikov VK (1963) On the stability of the center for time periodic perturbation. Trans Mosc Math Soc 12:1–57

    MathSciNet  Google Scholar 

  15. Wiggins S (1988) Global bifurcations and chaos-analytical methods. Springer, New York, pp 334–476

    Book  MATH  Google Scholar 

  16. Kovacic G, Wettergren TA (1996) Homoclinic orbits in the dynamics of resonantly driven coupled pendula. Z Angew Math Phys 47:221–264

    Article  MathSciNet  MATH  Google Scholar 

  17. Camassa R, Kovacic G, Tin SK (1998) A Melnikov method for homoclinic orbits with many pulse. Arch Ration Mech Anal 143:105–193

    Article  MathSciNet  MATH  Google Scholar 

  18. Haller G, Wiggins S (1995) N-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems. Arch Ration Mech Anal 130:25–101

    Article  MathSciNet  MATH  Google Scholar 

  19. Haller G, Wiggins S (1995) Multi-pulse jumping orbits and homoclinic trees in a modal truncation of the damped-forces nonlinear Schrodinger equation. Physica D 85:311–347

    Article  MathSciNet  MATH  Google Scholar 

  20. Haller G (1999) Chaos near resonance. Springer, New York

    Book  MATH  Google Scholar 

  21. Cao DX, Zhang W (2008) Global bifurcations and chaotic dynamics for a string-beam coupled system. Chaos Solit Fractals 37:858–875

    Article  MathSciNet  MATH  Google Scholar 

  22. Huangfu YG, Chen FQ (2013) Single-pulse chaotic dynamics of functionally graded materials plate. Acta Mech Sin 29:593–601

    Article  MathSciNet  MATH  Google Scholar 

  23. Zhang DM, Chen FQ (2017) Global bifurcations and single-pulse homoclinic orbits of a plate subjected to the transverse and in-plane excitations. Math Method Appl Sci 40:4338–4349

    Article  MathSciNet  MATH  Google Scholar 

  24. Li SB, Zhang W, Hao YX (2010) Multi-pulse chaotic dynamics of a functionally graded material rectangular plate with one-to-one internal resonance. Int J Nonlinear Sci Numer Stimul 11:351–362

    Article  MathSciNet  Google Scholar 

  25. Yao MH, Zhang W, Zu JW (2012) Multi-pulse chaotic dynamics in non-planar motion of parametrically excited viscoelastic moving belt. J Sound Vib 331:2624–2653

    Article  Google Scholar 

  26. Zhang W, Zheng Y, Liu T, Guo XY (2019) Multi-pulse jumping double-parameter chaotic dynamics of eccentric rotating ring truss antenna under combined parameteric and external excititations. Nonlinear Dyn 98:761–800

    Article  Google Scholar 

  27. Ma WS, Zhang W, Zhang YF (2021) Stability and multi-pulse jumping chaotic vibrations of a rotor-active magnetic bearing system with 16-pole legs under mechanical-electric-electromagnetic excitations. Eur J Mech A 85:104120

    Article  MathSciNet  MATH  Google Scholar 

  28. Malhotra N, Sri Namachchivaya N, McDonald RJ (2002) Multipulse orbits in the motion of flexible spinning discs. J Nonlinear Sci 12:1–26

    Article  MathSciNet  MATH  Google Scholar 

  29. Yao MH, Zhang W (2005) Multi-pulse Shilinov orbits and chaotic dynamics in nonlinear nonplanar motion of a cantilever beam. Int J Bifurc Chaos 15:3923–3952

    Article  MATH  Google Scholar 

  30. Zhang W, Yao MH (2006) Multi-pulse orbits and chaotic dynamics in motion of parametrically excited viscoelastic moving belt. Chaos Solitons Fractals 28:42–66

    Article  MathSciNet  MATH  Google Scholar 

  31. Yao MH, Zhang W (2007) Shilnikov type multi-pulse orbits and chaotic dynamics of a parametrically and excited rectangular thin plate. Int J Bifurc Chaos 17:851–875

    Article  MATH  Google Scholar 

  32. Yu TJ, Zhou S, Yang XD, Zhang W (2017) Global dynamics of composite panels with free-layer damping treatment in subsonic flow. Compos Struct 168:247–258

    Article  Google Scholar 

  33. Yu TJ, Zhou S, Zhang W, Yang XD (2017) Multi-pulse chaotic dynamics of an unbalanced Jeffcott rotor with gravity effect. Nonlinear Dyn 87:647–664

    Article  MATH  Google Scholar 

  34. Zhang YF, Yao MH, Zhang W, Wen BC (2017) Dynamical modeling and multi-pulse chaotic dynamics of cantilevered pipe conveying pulsating fluid in parametric resonance. Aerosp Sci Technol 68:441–453

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11902133).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Linyi University, Linyi, 276000, Shandong, China

    Dongmei Zhang & Yuanyuan Liu

Authors
  1. Dongmei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuanyuan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dongmei Zhang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, D., Liu, Y. Multi-pulse jumping orbits and chaos of a fluid-conveying functionally graded cylindrical shell under piezoelectric and parametric excitations. J Eng Math 138, 9 (2023). https://doi.org/10.1007/s10665-022-10254-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10665-022-10254-3

Keywords

Search

Navigation