Advertisement

Acta Mechanica Solida Sinica

, Volume 32, Issue 6, pp 737–753 | Cite as

Nonlinear Vibrations and Stability of an Axially Moving Plate Immersed in Fluid

  • Hongying LiEmail author
  • Tianyi Lang
  • Yongjun Liu
  • Jian Li
Article
  • 62 Downloads

Abstract

In this paper, the nonlinear forced vibrations and stability of an axially moving large deflection plate immersed in fluid are investigated. Based on von Kármán’s large deflection plate theory and taking into consideration the influence of fluid–structure interaction, axial moving and axial tension, nonlinear dynamic equations are obtained by applying D’Alembert’s principle. These dynamic equations are further discretized into ordinary differential equations via the Galerkin method. The frequency–response curves of system are obtained and examined. Then numerical method is used to analyze the bifurcation behaviors of immersed plate. Results show that as the parameters vary, the system displays periodic, multi-periodic, quasi-periodic and even chaotic motion. Through the analysis on global dynamic characteristics of fluid–structure interaction system, rich and varied nonlinear dynamic characteristics are obtained, and various ways that lead to chaotic motion of the system are further revealed.

Keywords

Axially moving plate Fluid–structure interaction Nonlinear vibrations Bifurcations 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11502050 and 11672072).

References

  1. 1.
    Lindholm US, Kana DD, Chu WH, Abramson HN. Elastic vibration characteristics of cantilever plates in water. J Ship Res. 1965;9:11–22.Google Scholar
  2. 2.
    Fu Y, Price WG. Interactions between a partially or totally immersed vibrating cantilever plate and the surrounding fluid. J Sound Vib. 1987;118:495–513.CrossRefGoogle Scholar
  3. 3.
    Ergin A, Uğurlu B. Linear vibration analysis of cantilever plates partially submerged in fluid. J Fluids Struct. 2003;17:927–39.CrossRefGoogle Scholar
  4. 4.
    Kerboua Y, Lakis AA, Thomas M, Marcouiller L. Vibration analysis of rectangular plates coupled with fluid. Appl Math Model. 2008;32:2570–86.CrossRefGoogle Scholar
  5. 5.
    Li J, Guo XH, Luo J, Li HY, et al. Analytical study on inherent properties of a unidirectional vibrating steel strip partially immersed in fluid. Shock Vib. 2013;20:793–807.CrossRefGoogle Scholar
  6. 6.
    Liao CY, Ma CC. Vibration characteristics of rectangular plate in compressible inviscid fluid. J Sound Vib. 2016;362:228–51.CrossRefGoogle Scholar
  7. 7.
    Khorshidi K, Akbari F, Ghadirian H. Experimental and analytical modal studies of vibrating rectangular plates in contact with a bounded fluid. Ocean Eng. 2017;140:146–54.CrossRefGoogle Scholar
  8. 8.
    Soni S, Jain NK, Joshi PV. Vibration analysis of partially cracked plate submerged in fluid. J Sound Vib. 2018;412:28–57.CrossRefGoogle Scholar
  9. 9.
    Dowell EH. Nonlinear flutter of rectangular plates. AIAA J. 1966;4:1267–75.CrossRefGoogle Scholar
  10. 10.
    Dowell EH. Nonlinear flutter of rectangular plates. II. AIAA J. 1967;5:1856–62.CrossRefGoogle Scholar
  11. 11.
    Ellen CH. The non-linear stability of panels in incompressible flow. J Sound Vib. 1977;54:117–21.CrossRefGoogle Scholar
  12. 12.
    Tubaldi E, Alijani F, Amabili M. Non-linear vibrations and stability of a periodically supported rectangular plate in axial flow. Int J Non Linear Mech. 2014;66:54–65.CrossRefGoogle Scholar
  13. 13.
    Tubaldi E, Amabili M, Alijani F. Nonlinear vibrations of plates in axial pulsating flow. J Fluids Struct. 2015;56:33–55.CrossRefGoogle Scholar
  14. 14.
    Li HY, Li J, Liu YJ. Internal resonance of an axially moving unidirectional plate partially immersed in fluid under foundation displacement excitation. J Sound Vib. 2015;358:124–41.CrossRefGoogle Scholar
  15. 15.
    Li HY, Li J, Lang TY, Zhu X. Dynamics of an axially moving unidirectional plate partially immersed in fluid under two frequency parametric excitation. Int J Non Linear Mech. 2018;99:31–9.CrossRefGoogle Scholar
  16. 16.
    Archibald FR, Emslie AG. The vibrations of a string having a uniform motion along its length. J Appl Mech. 1958;25:347–8.zbMATHGoogle Scholar
  17. 17.
    Chen LQ, Yang XD. Vibration and stability of an axially moving viscoelastic beam with hybrid supports. Eur J Mech A Solids. 2006;25:996–1008.MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wang XD. Numerical analysis of moving orthotropic thin plates. Comput Struct. 1999;70:467–86.CrossRefGoogle Scholar
  19. 19.
    Hatami S, Azhari M, Saadatpour MM. Free vibration of moving laminated composite plates. Compos Struct. 2007;80:609–20.CrossRefGoogle Scholar
  20. 20.
    Ghayesh MH, Amabili M, Païdoussis MP. Nonlinear dynamics of axially moving plates. J Sound Vib. 2013;332:391–406.CrossRefGoogle Scholar
  21. 21.
    Marynowski K, Kapitaniak T. Dynamics of axially moving continua. Int J Mech Sci. 2014;81:26–41.CrossRefGoogle Scholar
  22. 22.
    Banichuk N, Jeronen J, Neittaanmäki P, Tuovinen T. On the instability of an axially moving elastic plate. Int J Solids Struct. 2010;47:91–9.CrossRefGoogle Scholar
  23. 23.
    Mao XY, Ding H, Chen LQ. Forced vibration of axially moving beam with internal resonance in the supercritical regime. Int J Mech Sci. 2017;131–132:81–94.CrossRefGoogle Scholar
  24. 24.
    Marynowski K, Grabski J. Dynamic analysis of an axially moving plate subjected to thermal loading. Mech Res Commun. 2013;51:67–71.CrossRefGoogle Scholar
  25. 25.
    Li YH, Dong YH, Qin Y, Lv HW. Nonlinear forced vibration and stability of an axially moving viscoelastic sandwich beam. Int J Mech Sci. 2018;138–139:131–45.CrossRefGoogle Scholar
  26. 26.
    Ghayesh MH, Amabili M. Non-linear global dynamics of an axially moving plate. Int J Non Linear Mech. 2013;57:16–30.CrossRefGoogle Scholar
  27. 27.
    Yu TJ, Zhang W, Yang XD. Global bifurcations and chaotic motions of a flexible multi-beam structure. Int J Non Linear Mech. 2017;95:264–71.CrossRefGoogle Scholar
  28. 28.
    Ghayesh MH, Farokhi H. Global dynamics of imperfect axially forced microbeams. Int J Eng Sci. 2017;115:102–16.MathSciNetCrossRefGoogle Scholar
  29. 29.
    Xu F, Potier-Ferry M, Belouettar S, Hu H. Multiple bifurcations in wrinkling analysis of thin films on compliant substrates. Int J Non Linear Mech. 2015;76:203–22.CrossRefGoogle Scholar
  30. 30.
    Lakrad F, Belhaq M. Periodic solutions of strongly non-linear oscillators by the multiple scales method. J Sound Vib. 2002;258:677–700.MathSciNetCrossRefGoogle Scholar
  31. 31.
    Alijani F, Amabili M, Bakhtiari-Nejad F. On the accuracy of the multiple scales method for non-linear vibrations of doubly curved shallow shells. Int J Non Linear Mech. 2011;46:170–9.CrossRefGoogle Scholar
  32. 32.
    Alibakhshi A, Heidari H. Analytical approximation solutions of a dielectric elastomer balloon using the multiple scales method. Eur J Mech A Solids. 2019;74:485–96.MathSciNetCrossRefGoogle Scholar
  33. 33.
    Zhang M, Yang JP. Bifurcations and chaos in duffing equation. Acta Math Appl Sin. 2007;23:665–84.MathSciNetCrossRefGoogle Scholar
  34. 34.
    Cai MX, Cao HJ. Bifurcations of periodic orbits in Duffing equation with periodic damping and external excitations. Nonlinear Dyn. 2012;70:453–62.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2019

Authors and Affiliations

  • Hongying Li
    • 1
    Email author
  • Tianyi Lang
    • 1
  • Yongjun Liu
    • 1
  • Jian Li
    • 1
  1. 1.Institute of Applied Mechanics, College of ScienceNortheastern UniversityShenyangChina

Personalised recommendations