Nonlinear Dynamics

, Volume 74, Issue 4, pp 1267–1279

Nonlinear harmonic vibration analysis of a plate-cavity system

Original Paper

Abstract

Nonlinear harmonic oscillation of a plate-cavity system is analytically studied in this paper. Von-Karman theory is used to model a rectangular plate backed by an air cavity. Coupled nonlinear differential equations of system are analytically derived using Galerkin’s approach. The Multiple Scales Method (MSM) is then employed to solve the corresponding nonlinear equations. Primary, secondary, and combinational resonance conditions are taken into account and the corresponding closed-form frequency-amplitude relationships are derived. A parametric study is carried out and effects of different parameters on the frequency responses are investigated.

Keywords

Plate-cavity Resonance Nonlinear vibration Multiple scales method 

References

  1. 1.
    Frendi, A., Robinson, J.: Effect of acoustic coupling on random and harmonic plate vibrations. J. Acoust. Soc. Am. 31(11), 1992–1997 (1993) Google Scholar
  2. 2.
    Ding, W.P., Chen, H.L.: A symmetrical finite element model for structure-acoustic coupling analysis of an elastic, thin-walled cavity. J. Sound Vib. 243(3), 547–559 (2001) MathSciNetCrossRefGoogle Scholar
  3. 3.
    Li, Y.Y., Cheng, L.: Vibro-acoustic analysis of a rectangular-like cavity with a tilted wall. Appl. Acoust. 68, 739–751 (2007) CrossRefGoogle Scholar
  4. 4.
    Lee, Y.: Structural-acoustic coupling effect on the nonlinear natural frequency of a rectangular box with one flexible plate. Appl. Acoust. 63, 1157–1175 (2002) CrossRefGoogle Scholar
  5. 5.
    Lee, Y., Guo, X., Hui, C., Lau, C.: Nonlinear multi-modal structural/acoustic interaction between a composite plate vibration and the induced pressure. Int. J. Nonlinear Sci. Numer. Simul. 9(3), 221–228 (2008) CrossRefGoogle Scholar
  6. 6.
    Lee, Y., Li, Q., Leung, A.Y., Su, R.K.: The jump phenomenon effect on the sound absorption of a nonlinear panel absorber and sound transmission loss of a nonlinear panel backed by a cavity. Nonlinear Dyn. 69, 1–18 (2012) MathSciNetCrossRefGoogle Scholar
  7. 7.
    Lee, Y.: Analysis of the nonlinear structural-acoustic resonant frequencies of a rectangular tube with a flexible end using harmonic balance and homotopy perturbation methods. Abstract Appl. Anal. Article ID 391584 (2012). doi:10.1155/2012/391584
  8. 8.
    Lee, Y., Huang, J., Hui, C., Ng, C.: Sound absorption of a quadratic and cubic nonlinearly vibrating curved panel absorber. Appl. Math. Model. 36, 5574–5588 (2012) MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Tanaka, N., Takara, Y., Iwamoto, H.: Eigenpairs of a coupled rectangular cavity and its fundamental properties. J. Acoust. Soc. Am. 131, 1910–1921 (2012) CrossRefGoogle Scholar
  10. 10.
    Park, S.Y., Kim, S.H., Kang, Y.J.: The effect of a local stiffener in the structural—acoustic coupled system. Proc. Inst. Mech. Eng., Part C, J. Mech. Eng. Sci. 224, 1915–1931 (2010) CrossRefGoogle Scholar
  11. 11.
    Luo, C., Zhao, M., Rao, Z.: The analysis of structural-acoustic coupling of an enclosure using Green’s function method. Int. J. Adv. Manuf. Technol. 27, 242–247 (2005) CrossRefGoogle Scholar
  12. 12.
    Lee, Y.Y., Guo, X., Hui, C.K., Lau, C.M.: Nonlinear multi-modal structural/acoustic interaction between a composite plate vibration and the induced pressure. Int. J. Nonlinear Sci. Numer. Simul. 9, 221–228 (2008) CrossRefGoogle Scholar
  13. 13.
    Venkatesham, B., Tiwari, M., Munjal, M.L.: Analytical prediction of the breakout noise from a rectangular cavity with one compliant wall. J. Acoust. Soc. Am. 124, 2952–2962 (2008) CrossRefGoogle Scholar
  14. 14.
    Lam, H.F., Ng, C.T., Lee, Y.Y., Sun, H.Y.: System identification of an enclosure with leakages using a probabilistic approach. J. Sound Vib. 322, 756–771 (2009) CrossRefGoogle Scholar
  15. 15.
    Sadri, M., Younesian, D.: Nonlinear free vibration analysis of a plate-cavity system. Thin Walled Struct. (2013, accepted) Google Scholar
  16. 16.
    Younesian, D., Askari, H., Saadatnia, Z.: Analytical solutions for free oscillation of beams on nonlinear elastic foundations using the variational iteration method. J. Theor. Appl. Mech. 50, 639–652 (2012) Google Scholar
  17. 17.
    Balachandran, B., Sampath, A., Park, J.: Active control of interior noise in a three-dimensional enclosure. Smart Mater. Struct. 5, 89–97 (1996) CrossRefGoogle Scholar
  18. 18.
    Al-Bassyiouni, M., Balachandran, B.: Sound transmission through a flexible panel into an enclosure: structural-acoustics model. J. Sound Vib. 284, 467–486 (2005) CrossRefGoogle Scholar
  19. 19.
    Bécot, F.X., Sgard, F.: On the use of poroelastic materials for the control of the sound radiated by a cavity backed plate. J. Acoust. Soc. Am. 120, 2055–2066 (2006) CrossRefGoogle Scholar
  20. 20.
    Hill, S.G., Tanaka, N., Snyder, S.D.: A generalized approach for active control of structural-interior global noise. J. Sound Vib. 326, 456–475 (2009) CrossRefGoogle Scholar
  21. 21.
    Younesian, D., Esmailzadeh, E., Sedaghati, R.: Existence of periodic solutions for the generalized form of Mathieu equation. Nonlinear Dyn. 39(4), 335–348 (2005) MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Younesian, D., Marjani, S.R., Esmailzadeh, E.: Nonlinear vibration analysis of harmonically excited cracked beams on viscoelastic foundations. Nonlinear Dyn. 71(1–2), 109–112 (2013) MathSciNetCrossRefGoogle Scholar
  23. 23.
    Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley-VCH, Weinheim (1995) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Center of Excellence in Railway Transportation, School of Railway EngineeringIran University of Science and TechnologyTehranIran

Personalised recommendations