Advertisement

Analytical Modelling of Sound Transmission Through Finite Clamped Double-Wall Panels with Magnetic-Linked Stiffness

  • Akintoye Olumide OyeladeEmail author
Original Paper
  • 20 Downloads

Abstract

A theoretical modelling approach is proposed for the vibroacoustic problem of sound transmission across a rectangular double-wall panel clamp mounted on an infinite rigid baffle with magnetically connected stiffness. The magnetic stiffness is derived based on interaction energy between the two rectangular magnets attached to the clamped plates. The exact solution for the vibration of the clamped double plates is taken into account by the method of modal function, and the dynamic response of the structures is obtained by employing the weighted residual (Galerkin) method. This method enabled the coupling of the acoustic and the magnetic stiffness of the link to be done effectively. The accuracy of the theoretical predictions is checked against existing experimental data, with good agreement achieved. The model is then compared with the theoretical formulation in a duct based on a low-frequency range with and without magnetic stiffness. The sound transmission loss (STL) of the two models agrees perfectly in the first resonance, but the mass–air–mass resonance frequency for the current model tends to shift towards a higher value. Furthermore, the influence of magnetic stiffness on the elevation angle and azimuth angle of the STL is investigated. The present method is suitable for double-panel systems with connecting stiffness for practical plates and is applicable for both low- and high-frequency ranges.

Keywords

Sound transmission loss Magnetic stiffness Clamped boundary Rigid duct 

Notes

Acknowledgements

The author would like to thank Professor Yu Liu of the Department of Mechanics Southern University of Science of Technology, Shenzhen, for providing means of verification of this work.

References

  1. 1.
    Brekket, A.: Calculation methods for the transmission loss of single, double and triple partitions. Appl. Acousrrcs 14, 225–240 (1981)CrossRefGoogle Scholar
  2. 2.
    Tadeu, A., António, J., Mateus, D.: Sound insulation provided by single and double panel walls: a comparison of analytical solutions versus experimental results. Appl. Acoust. 65, 15–29 (2004)CrossRefGoogle Scholar
  3. 3.
    Legault, J., Atalla, N.: Sound transmission through a double panel structure periodically coupled with vibration insulators. J. Sound Vib. 329, 3082–3100 (2010)CrossRefGoogle Scholar
  4. 4.
    Xin, F.X., Lu, T.J., Chen, C.Q.: Vibroacoustic behavior of clamp mounted double-panel partition with enclosure air cavity. J. Acoust. Soc. Am. 124, 3604–3612 (2008)CrossRefGoogle Scholar
  5. 5.
    Kropp, W., Rebillard, E.: On the air-borne sound insulation of double wall constructions. Acustica 85(5), 707–720 (1999)Google Scholar
  6. 6.
    António, J.M.P., Tadeu, A., Godinho, L.: Analytical evaluation of the acoustic insulation provided by double infinite walls. J. Sound Vib. 263, 113–129 (2003)CrossRefGoogle Scholar
  7. 7.
    Wang, J., Lu, T.J., Woodhouse, J., Langley, R.S., Evans, J.: Sound transmission through lightweight double-leaf partitions: theoretical modelling. J. Sound Vib. 286, 817–847 (2005)CrossRefGoogle Scholar
  8. 8.
    Price, A.J.: Sound transmission through double panels using statistical energy analysis. J. Acoust. Soc. Am. 47, 683 (1970)CrossRefGoogle Scholar
  9. 9.
    Cheng, L., Li, Y.Y., Gao, J.X.: Energy transmission in a mechanically-linked double-wall structure coupled to an acoustic enclosure. J. Acoust. Soc. Am. 117, 2742–2751 (2005)CrossRefGoogle Scholar
  10. 10.
    Li, Y.Y., Cheng, L.: Energy transmission through a double-wall structure with an acoustic enclosure: rotational effect of mechanical links. Appl. Acoust. 67, 185–200 (2006)CrossRefGoogle Scholar
  11. 11.
    Liu, Y., Daudin, C.: Analytical modelling of sound transmission through finite clamped double-wall sandwich panels lined with poroelastic materials. Compos. Struct. 172, 359–373 (2017)CrossRefGoogle Scholar
  12. 12.
    Panneton, R., Atalla, N.: Numerical prediction of sound transmission through finite multilayer systems with poroelastic materials. J. Acoust. Soc. Am. 100, 346–354 (1996)CrossRefGoogle Scholar
  13. 13.
    Xin, F.X., Lu, T.J.: Effects of core topology on sound insulation performance of lightweight all-metallic sandwich panels. Mater. Manuf. Process. 26, 1213–1221 (2011)CrossRefGoogle Scholar
  14. 14.
    Yang, H., Zheng, H., Xie, X.: Sound transmission through a double-wall structure coupled with two trapezoidal acoustic cavities. Int. J. Appl. Mech. (2016).  https://doi.org/10.1142/s1758825116501003 Google Scholar
  15. 15.
    Leppington, F.G., Broadbent, E.G., Butler, G.F.: Transmission of sound through a pair of rectangular elastic plates. IMA J. Appl. Math. 71, 940–955 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Chazot, J.D., Guyader, J.L.: Prediction of transmission loss of double panels with a patch-mobility method. J. Acoust. Soc. Am. 121, 267–278 (2007)CrossRefGoogle Scholar
  17. 17.
    Gardonio, P., Elliott, S.J.: Active control of structure-borne and airborne sound transmission through double panel. J. Aircr. 36, 1023–1032 (1999)CrossRefGoogle Scholar
  18. 18.
    Patricio, A.L., Bernard, F.S.: Study of small-amplitude vibrations of clamped rectangular plates using polynomial approximations. J. Acoust. Soc. Am. 41(4), 836–839 (1967)Google Scholar
  19. 19.
    Carneal, J.P., Fuller, C.R.: Active structural acoustic control of noise transmission through double panel systems. AIAA 33, 618–623 (1995)CrossRefGoogle Scholar
  20. 20.
    Oyelade, A.O., Chen, Y., Zhang, R., Hu, G.: Analytical and experimental investigation on sound transmission of double thin plates with magnetic negative stiffness. Int. J. Appl. Mech. 10, 1850054-1 (2018)CrossRefGoogle Scholar
  21. 21.
    Yonnet, J.P., Allag, H.: Three-dimensional analytical calculation of permanent magnet interactions by ‘magnetic node’ representation. IEEE Trans. Magn. 47, 2050–2055 (2011)CrossRefGoogle Scholar
  22. 22.
    Essink, B.C., Hobeck, J.D., Owen, R.B., Inman, D.J.: Magnetoelastic energy harvester for structural health monitoring applications. Int. Soc. Opt. Photon. 9431, 943123 (2015)Google Scholar
  23. 23.
    Carrella, A., Brennan, M.J., Waters, T.P.: Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vib. 301, 678–689 (2007)CrossRefGoogle Scholar
  24. 24.
    Carrella, A., Brennan, M.J., Waters, T.P., Shin, K.: On the design of a high-static-low-dynamic stiffness isolator using linear mechanical springs and magnets. J. Sound Vib. 315, 712–720 (2008)CrossRefGoogle Scholar
  25. 25.
    Oyelade, A.O., Wang, Z., Hu, G.: Dynamics of 1D mass-spring system with a negative stiffness spring realized by magnets: theoretical and experimental study. Theor. Appl. Mech. Lett. 7, 17–21 (2017)CrossRefGoogle Scholar
  26. 26.
    Wu, W., Chen, X., Shan, Y.: Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness. J. Sound Vib. 333, 2958–2970 (2014)CrossRefGoogle Scholar
  27. 27.
    Akoun, G., Yonnet, J.-P.: 3D analytical calculation of the forces exerted between two cuboidal magnets. IEEE Trans. Magn. 20, 1962–1964 (1984)CrossRefGoogle Scholar
  28. 28.
    Xin, F.X., Lu, T.J.: Analytical and experimental investigation on transmission loss of clamped double panels: implication of boundary effects. J. Acoust. Soc. Am. 125, 1506–1517 (2009)CrossRefGoogle Scholar
  29. 29.
    Meng, H., Xin, F.X., Lu, T.J.: External mean flow effects on sound transmission through acoustic absorptive sandwich structure. AIAA J. 50, 2268–2276 (2012)CrossRefGoogle Scholar
  30. 30.
    Carneal, J.P., Fuller, C.R.: An analytical and experimental investigation of active structural acoustic control of noise transmission through double panel systems. J. Sound Vib. 272, 749–771 (2004)CrossRefGoogle Scholar
  31. 31.
    Xin, F.X., Lu, T.J.: Analytical modeling of sound transmission across finite aeroelastic panels in convicted fluids. J. Acoust. Soc. Am. 128, 1097–1107 (2010)CrossRefGoogle Scholar

Copyright information

© Australian Acoustical Society 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of LagosAkoka, LagosNigeria

Personalised recommendations