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Nonlinear vibration analysis of a circular plate–cavity system

  • Fatemeh Sadat Anvariyeh
  • Mohammad Mahdi JaliliEmail author
  • Ali Reza Fotuhi
Technical Paper
  • 40 Downloads

Abstract

Vibration of plate with air cavity has been one of the interesting research fields by many researchers. This topic has many applications in vehicles, airplanes, aircraft, fuselage panels and buildings. In this study, nonlinear vibroacoustic of circular plate with air cavity under harmonic excitation is investigated. The von Karman theory is used to obtain plate equation and solved together with the air pressure equation. First, the nonlinear equation of the plate is converted to ordinary differential equations by using the Galerkin method. Then the method of multiple scales is employed to solve the corresponding nonlinear equations. Frequency response for primary, subharmonic and superharmonic resonances is studied analytically. Using this method, a parametric study is carried out and the effects of different parameters on the frequency response of the plate are investigated. According to the results, jump phenomena are observed for primary and superharmonic resonance cases. Also, with an increase in damping coefficient, the amplitude of the steady-state response increases in the subharmonic resonance case.

Keywords

Vibroacoustic Nonlinear oscillation Circular plate Harmonic excitation Multiple scales method 

Abbreviations

c

Depth of acoustic enclosure

ca

Sound speed

cd

Structural damping coefficient

D

Bending stiffness

E

Young’s modulus of elasticity

h

Thickness

Pi

Acoustic pressure

PE

External excitation

φ

Airy stress function

ρ

Density

ν

Poisson’s ratio

σ

Detuning parameter

Ω

Excitation frequency

ωn

Natural frequency

References

  1. 1.
    Lyon RH (1963) Noise reduction of rectangular enclosures with one flexible wall. J Acoust Soc Am 35:1791–1797CrossRefGoogle Scholar
  2. 2.
    Pretlove AJ (1965) Free vibration of a rectangular panel backed by a closed rectangular cavity. J Sound Vib 2(3):197–209CrossRefGoogle Scholar
  3. 3.
    Pretlove AJ (1966) Forced vibration of a rectangular panel backed by a closed rectangular cavity. J Sound Vib 3(3):252–261CrossRefGoogle Scholar
  4. 4.
    Qaisi MI (1988) Free vibrations of a rectangular plate–cavity system. Appl Acoust 24:49–61CrossRefGoogle Scholar
  5. 5.
    Lee YY (2002) Structural-acoustic coupling effect on the nonlinear natural frequency of a rectangular box with one flexible plate. Appl Acoust 63:1157–1175CrossRefGoogle Scholar
  6. 6.
    Xin FX, Lu TJ, Chen CQ (2008) Vibroacoustic behavior of clamp mounted double-panel partition with enclosure air cavity. J Acoust Soc Am 124(6):3604–3612CrossRefGoogle Scholar
  7. 7.
    Luo C, Zhao M, Rao Z (2005) The analysis of structural-acoustic coupling of an enclosure using Green’s function method. Int J Adv Manuf Technol 27:242–247CrossRefGoogle Scholar
  8. 8.
    Lee YY, Guo X, Hui CK, Lau CM (2008) Nonlinear multi-modal structural acoustic interaction between a composite plate vibration and the induced pressure. Int J Nonlinear Sci Numer 9(3):221–228MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lee YY (2012) Analysis of the nonlinear structural-acoustic resonant frequencies of a rectangular tube with a flexible end using harmonic balance and homotopy perturbation methods. Abstr Appl Anal 2012:1–13Google Scholar
  10. 10.
    Lee YY, Huang JL, Hui CK, Ng CF (2012) Sound absorption of a quadratic and cubic nonlinearly vibrating curved panel absorber. Appl Math Model 36:5574–5588MathSciNetCrossRefGoogle Scholar
  11. 11.
    Lee YY, Li QS, Leung AYT, Su RKL (2012) 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 69:99–116MathSciNetCrossRefGoogle Scholar
  12. 12.
    Shi SX, Jin GY, Liu ZGC (2014) Vibro-acoustic behaviors of an elastically restrained double-panel with an acoustic cavity of arbitrary boundary impedance. Appl Acoust 76:431–444CrossRefGoogle Scholar
  13. 13.
    Pirnat M, Čepon G, Boltežar M (2014) Structural–acoustic model of a rectangular plate–cavity system with an attached distributed mass and internal sound source: theory and experiment. J Sound Vib 333:2003–2018CrossRefGoogle Scholar
  14. 14.
    Chen Y, Jin G, Shi S, Liu Z (2014) A general analytical method for vibroacoustic analysis of an arbitrarily restrained rectangular plate backed by a cavity with general wall impedance. J Vib Acoust 136:1–11Google Scholar
  15. 15.
    Sadri M, Younesian D (2014) Nonlinear free vibration analysis of a plate–cavity system. Thin Wall Struct 74:191–200CrossRefGoogle Scholar
  16. 16.
    Sadri M, Younesian D (2013) Nonlinear harmonic vibration analysis of a plate–cavity system. J Nonlinear Dyn 74:1267–1279CrossRefGoogle Scholar
  17. 17.
    Jalili MM, Emami H (2017) Analytical solution for nonlinear oscillation of workpiece in turning process. Proc Inst Mech Eng Part C J Mech Eng Sci 231:3479–3492CrossRefGoogle Scholar
  18. 18.
    Jalili MM, Fazel R, Abootorabi MM (2017) Simulation of chatter in plunge grinding process with structural and cutting force nonlinearities. Int J Adv Manuf Technol 89:2863–2881CrossRefGoogle Scholar
  19. 19.
    Jalili MM, Hesabi J, Abootorabi MM (2017) Simulation of forced vibration in milling process considering gyroscopic moment and rotary inertia. Int J Adv Manuf Technol 89:2821–2836CrossRefGoogle Scholar
  20. 20.
    Masoomi M, Jalili MM (2016) Non-linear vibration analysis of a 2-DOF railway vehicle model under random rail excitation. P I Mech Eng K-J Mul 231:591–607Google Scholar
  21. 21.
    Rajalingham C, Bhat RB, Xistris GD (1998) Vibration of circular membrane backed by cylindrical cavity. Int J Mech Sci 40(8):723–734CrossRefGoogle Scholar
  22. 22.
    Lee YY (2003) Insertion loss of a cavity-backed semi-cylindrical enclosure panel. J Sound Vib 259:625–636CrossRefGoogle Scholar
  23. 23.
    Gorman DG, Lee CK, Reese JM, Wek JH (2005) Vibration analysis of a thin circular plate influenced by liquid/gas interaction in a cylindrical cavity. J Sound Vib 279:601–618CrossRefGoogle Scholar
  24. 24.
    Gorman DG, Trendafilova I, Mulholland AJ, Horáček J (2008) Vibration analysis of a circular plate in interaction with an acoustic cavity leading to extraction of structural modal parameters. Thin Wall Struct 46:878–886CrossRefGoogle Scholar
  25. 25.
    Gorman DG, Reese JM, HoraÂcek J, Dedouch K (2008) Vibration analysis of a circular disc backed by a cylindrical cavity. Proc Inst Mech Eng Part C J Mech Eng Sci 215(11):1303–1311CrossRefGoogle Scholar
  26. 26.
    Amabili M (1997) Bulging modes of circular bottom plates in rigid cylindrical containers filled with a liquid. Shock Vib 4:51–68CrossRefGoogle Scholar
  27. 27.
    Amabili M (2001) Vibrations of circular plates resting on a sloshing liquid: solution of the fully coupled problem. J Sound Vib 245:261–283CrossRefGoogle Scholar
  28. 28.
    Jeong KH, Kim KJ (2005) Hydroelastic vibration of a circular plate submerged in a bounded compressible fluid. J Sound Vib 283:153–172CrossRefGoogle Scholar
  29. 29.
    Askari E, Jeong KH, Amabili M (2013) Hydroelastic vibration of circular plates immersed in a liquid-filled container with free surface. J Sound Vib 332:3064–3085CrossRefGoogle Scholar
  30. 30.
    Tariverdilo S, Shahmardani M, Mirzapour J, Shabani R (2013) Asymmetric free vibration of circular plate in contact with incompressible fluid. Appl Math Model 37:228–239MathSciNetCrossRefGoogle Scholar
  31. 31.
    Rdzanek WP, Rdzanek WJ, Szemela K (2016) Sound radiation of the resonator in the form of a vibrating circular plate embedded in the outlet of the circular cylindrical cavity. J Comput Acoust 24:165–183MathSciNetCrossRefGoogle Scholar
  32. 32.
    Escaler X, De La Torre O (2018) Axisymmetric vibrations of a circular Chladni plate in air and fully submerged in water. J Fluids Struct 82:432–445CrossRefGoogle Scholar
  33. 33.
    Eftekhari SA (2016) Pressure-Based and potential-based differential quadrature procedures for free vibration of circular plates in contact with fluid. Lat Am J Solids Struct 13:610–631CrossRefGoogle Scholar
  34. 34.
    Hasheminejad SM, Shakeri R (2017) Active transient acousto-structural response control of a smart cavity-coupled circular plate system. Arch Acoust 42:273–286CrossRefGoogle Scholar
  35. 35.
    Szemela K (2018) Sound radiation by a cylindrical open cavity with a surface source at the bottom. Arch Acoust 43:49–60Google Scholar
  36. 36.
    Reddy JN (2007) Theory and analysis of elastic plates and shells, 2nd edn. CRC Press, Boca RatonGoogle Scholar
  37. 37.
    Nayfeh AH, Pai PF (2004) Linear and nonlinear structural mechanics, 1st edn. Wiley, New JerseyCrossRefGoogle Scholar
  38. 38.
    Nayfeh AH, Mook D (1979) Nonlinear oscillations. Wiley, New YorkzbMATHGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringYazd UniversityYazdIran

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