Acoustical Physics

, Volume 64, Issue 5, pp 643–650 | Cite as

A Simplified Method for Calculating Multilayer Sound Insulation with Layers of Fibrous Porous Material

  • L. R. YablonikEmail author

Abstract—The proposed method is based on the Biot theory of wave propagation in porous saturated elastic media. To simplify the cumbersome full calculation procedure, specific features of typical fibrous porous materials are used: a large density and moderate stiffness of the elastic frame in comparison to air. In this case, the transfer properties of an elastic porous layer are represented by two second-order matrices, which characterize sound transfer by airborne and frame-borne waves. Combined with the boundary conditions, such a representation in standard schemes makes it possible to form a single transfer matrix for the layer, by considering it a linear four-pole that relates the pressures and normal velocity components at the inlet and exit. When calculating the sound insulation of a multilayer structure, the formed matrix of the elastic porous layer is introduced via a cofactor into a chain of second-order transfer matrices determined by the other layers. Examples and comparative calculations are presented that demonstrate the high correspondence of the method’s results to the full calculation data.


Biot theory airborne and frame-borne waves partial decoupling four-pole matrix 



  1. 1.
    M. A. Biot, J. Acoust. Soc. Am. 28, 168 (1956).ADSCrossRefGoogle Scholar
  2. 2.
    M. A. Biot and D. G. Willis, J. Appl. Mech. 24, 594 (1957).MathSciNetGoogle Scholar
  3. 3.
    N. N. Knyaz’kov and B. P. Sharfarets, Nauchn. Priborostr. 26 (1), 77 (2016).CrossRefGoogle Scholar
  4. 4.
    N. Atalla, R. Panneton, and P. Debergue, J. Acoust. Soc. Am. 104, 1444 (1998).ADSCrossRefGoogle Scholar
  5. 5.
    O. Dazel, B. Brouard, C. Depollier, and S. Griffiths, J. Acoust. Soc. Am. 121, 3509 (2007).ADSCrossRefGoogle Scholar
  6. 6.
    J. H. Lee and J. Kim, J. Acoust. Soc. Am. 110, 2282 (2001).ADSCrossRefGoogle Scholar
  7. 7.
    H. Liu, S. Finnveden, M. Barbagallo, and I. L. Arteaga, J. Acoust. Soc. Am. 135, 2683 (2014).ADSCrossRefGoogle Scholar
  8. 8.
    J. F. Allard and N. Atalla, Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials, 2nd ed. (John Wiley and Sons, 2009).Google Scholar
  9. 9.
    L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Vol. 7 of Course of Theoretical Physics (Nauka, Moscow, 1965; Pergamon Press, Oxford, 1970).Google Scholar
  10. 10.
    P. N. Kravchun, Generation and Methods for Reducing Noise and Sound Vibration (Moscow State Univ., Moscow, 1991) [in Russian].Google Scholar
  11. 11.
    L. R. Yablonik, Tr. Nauchno-Proizvod. Ob’edin. Issled. Proekt. Energ. Oborud. im. I. I. Polzunova, No. 292, 104 (2003).Google Scholar
  12. 12.
    Sound Insulation and Sound Absorbing, Ed. by L. G. Osipov and V. N. Bobylev (AST-Astrel’, Moscow, 2004) [in Russian].Google Scholar
  13. 13.
    D. L. Johnson, J. Koplik, and R. Dashen, J. Fluid Mech. 176, 379 (1987).ADSCrossRefGoogle Scholar
  14. 14.
    Y. Champoux and J. F. Allard, J. Appl. Phys. 70, 1975 (1991).ADSCrossRefGoogle Scholar
  15. 15.
    M. E. Delany and E. N. Bazley, Appl. Acoust. 3, 105 (1970).CrossRefGoogle Scholar
  16. 16.
    A. A. Belous, A. I. Korol’kov, and A. V. Shanin, Acoust. Phys. 64 (2), 158 (2018).ADSCrossRefGoogle Scholar
  17. 17.
    Y. Liu, X. Liu, J. Xu, X. Hu, and Z. Xia, J. Acoust. Soc. Am. 142, 72 (2017).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Polzunov Scientific and Development Association on Research and Design of Power EquipmentSt. PetersburgRussia

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