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On the Use of Transfer Approaches to Predict the Vibroacoustic Response of Poroelastic Media

Université d’Orléans, Laboratoire PRISME, Orléans, France

École Centrale de Lyon, Laboratoire de Tribologie et de Dynamique des Sysèmes, Écully 69130, France

Conservatoire National des Arts et Métiers, Laboratoire des Mécanique des Structures et des Systèmes Couplés, Paris 75003, France

E-mail Address: [email protected]

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M. N. Ichchou

École Centrale de Lyon, Laboratoire de Tribologie et de Dynamique des Sysèmes, Écully 69130, France

E-mail Address: [email protected]

Corresponding author.

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J.-F. Deü

Conservatoire National des Arts et Métiers, Laboratoire des Mécanique des Structures et des Systèmes Couplés, Paris 75003, France

E-mail Address: [email protected]

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https://doi.org/10.1142/S0218396X15500204Cited by:5 (Source: Crossref)

Abstract

The transfer matrix method (TMM) is a famous analytic method in the vibroacoustic community. It is classically considered as a high frequency approach, because of the hypothesis of acoustic plane waves impinging on a flat infinite panel. Thus, it cannot take into account directly finite-size effects or lateral boundary conditions (BCs), and it needs specific algorithms to correct its results in the low frequency range. Within the transfer matrix framework, the use of finite elements makes it possible to generalize the range of applications of transfer approaches. Thus, the study of wave propagation in poroelastic media, in presence of lateral BCs can be carried out. The links between theses waves and the acoustic response of a sample are investigated. Finally, it shows that transfer approaches are not limited in the low frequency range, as usually stated. In fact, the validity of analytic transfer approaches depends more on the material and on the geometry than on the frequency range.

Keywords:

References

1. W. T. Thomson, Transmission of elastic waves through a stratified solid medium, J. Appl. Phys. 21(2) (1950) 89–93. Crossref, Web of Science, Google Scholar
2. N. A. Haskell, The dispersion of surface waves on multilayered media, Bull. Seismol. Soc. Am. 43(1) (1953) 17–34. Crossref, Google Scholar
3. J.-F. Allard and N. Atalla, Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials, 2nd edn. (Wiley, New York, 2009). Crossref, Google Scholar
4. B. Brouard, D. Lafarge and J.-F. Allard, A general method of modelling sound propagation in layered media, J. Sound Vibr. 183(1) (1995) 129–142. Crossref, Web of Science, Google Scholar
5. N. Atalla, R. Panneton and P. Debergue, A mixed displacement-pressure Formulation for poroelastic materials, J. Acoust. Soc. Am. 104(3) (1998) 1444–1452. Crossref, Web of Science, Google Scholar
6. P. Göransson, A 3-D, symmetric, finite element formulation of the Biot equations with application to acoustic wave propagation through an elastic porous medium, Int. J. Numer. Methods Eng. 41(1) (1998) 167–192. Crossref, Web of Science, Google Scholar
7. F. Chevillotte and R. Panneton, Coupling transfer matrix method to finite element method for analyzing the acoustics of complex hollow body networks, Appl. Acoust. 72(12) (2011) 962–968. Crossref, Web of Science, Google Scholar
8. L. Alimonti, N. Atalla, A. Berry and F. Sgard, A hybrid modeling approach for vibroacoustic systems with attached sound packages, in Proc. Meetings on Acoustics, Vol. 19, 7 June 2013, Montréal, Canada, 2013, pp. 1–9. Google Scholar
9. A. Dijckmans and G. Vermeir, Development of a hybrid wave based–transfer matrix model for sound transmission analysis, J. Acoust. Soc. Am. 133(4) (2013) 2157–2168. Crossref, Web of Science, Google Scholar
10. M. Villot, C. Guigou and L. Gagliardini, Predicting the acoustical radiation of finite size multi-layered structures by applying spatial windowing on infinite structures, J. Sound Vibr. 245(3) (2001) 433–455. Crossref, Web of Science, Google Scholar
11. D. Rhazi and N. Atalla, A simple method to account for size effects in the transfer matrix method, J. Acoust. Soc. Am. 127(2) (2010) 30–36. Crossref, Web of Science, Google Scholar
12. J.-M. Mencik and M. N. Ichchou, Multi-mode propagation and diffusion in structures through finite elements, Eur. J. Mech. A. Solids 24(5) (2005) 877–898. Crossref, Web of Science, Google Scholar
13. B. R. Mace, D. Duhamel, M. J. Brennan and L. Hinke, Finite element prediction of wave motion in structural waveguides, J. Acoust. Soc. Am. 117(5) (2005) 2835–2843. Crossref, Web of Science, Google Scholar
14. Y. J. Kang and J. S. Bolton, Finite element modeling of isotropic elastic porous materials coupled with acoustical finite elements, J. Acoust. Soc. Am. 98(1) (1995) 635–643. Crossref, Web of Science, Google Scholar
15. B. H. Song, J. S. Bolton and Y. J. Kang, Effect of circumferential edge constraint on the acoustical properties of glass fiber materials, J. Acoust. Soc. Am. 110(6) (2001) 2902–2916. Crossref, Web of Science, Google Scholar
16. H. Aygun and K. Attenborough, Sound absorption by clamped poroelastic plates, J. Acoust. Soc. Am. 124(3) (2008) 1550–1556. Crossref, Web of Science, Google Scholar
17. M. A. Biot, Mechanics of deformation and acoustic propagation in porous media, J. Appl. Phys. 33(4) (1962) 1482–1498. Crossref, Web of Science, Google Scholar
18. N. Atalla, M. A. Hamdi and R. Panneton, Enhanced weak integral formulation for the mixed (u, p) poroelastic equations, J. Acoust. Soc. Am. 109(6) (2001) 3065–3068. Crossref, Web of Science, Google Scholar
19. O. Dazel, B. Brouard, C. Depollier and S. Griffiths, An alternative Biot’s displacement formulation for porous materials, J. Acoust. Soc. Am. 121(6) (2007) 3509–3516. Crossref, Web of Science, Google Scholar
20. A. Benjeddou and J.-F. Deü, Piezoelectric transverse shear actuation and sensing of plates, Part 1: A three-dimensional mixed state space formulation, J. Intell. Mater. Syst. Struct. 12(7) (2001) 435–449. Crossref, Web of Science, Google Scholar
21. D. Duhamel, B. R. Mace and M. J. Brennan, Finite element analysis of the vibrations of waveguides and periodic structures, J. Sound Vibr. 294(1) (2006) 205–220. Crossref, Web of Science, Google Scholar
22. G. Gosse, C. Pézerat and F. Bessac, Vibroacoustique d’une structure périodique de type batterie à ailettes, in Actes du 10ème Congrès Francais d’Acoustique (SFA Paris, Lyon, France, 2010), pp. 1–5. Google Scholar
23. L. Houillon, M. N. Ichchou and L. Jezequel, Wave motion in thin-walled structures, J. Sound Vibr. 281(3) (2005) 483–507. Crossref, Web of Science, Google Scholar
24. B. R. Mace and E. Manconi, Modelling wave propagation in two-dimensional structures using finite element analysis, J. Sound Vibr. 318(4) (2008) 884–902. Crossref, Web of Science, Google Scholar
25. E. Manconi and S. Sorokin, On the effect of damping on dispersion curves in plates, Int. J. Solids Struct. 50(11–12) (2013) 1966–1973. Crossref, Web of Science, Google Scholar
26. M. A. Ben Souf, O. Bareille, M. N. Ichchou, F. Bouchoucha and M. Haddar, Waves and energy in random elastic guided media through the stochastic wave finite element method, Phys. Lett. A 377(37) (2013) 2255–2264. Crossref, Web of Science, Google Scholar
27. D. Chronopoulos, B. Troclet, O. Bareille and M. N. Ichchou, Modeling the response of composite panels by a dynamic stiffness approach, Compos. Struct. 96 (2013) 111–120. Crossref, Web of Science, Google Scholar
28. C. Droz, J.-P. Lainé, M. N. Ichchou and G. Inquiété, A reduced formulation for the free-wave propagation analysis in composite structures, Compos. Struct. 113 (2013) 134–144. Crossref, Web of Science, Google Scholar
29. Q. Serra, M. N. Ichchou and J.-F. Deü, Wave properties in poroelastic media using a wave finite element method, J. Sound Vibr. 335 (2015) 125–146. Crossref, Web of Science, Google Scholar
30. Y. Waki, B. R. Mace and M. J. Brennan, Free and forced vibrations of a tyre using a wave/finite element approach, J. Sound Vibr. 323(3) (2009) 737–756. Crossref, Web of Science, Google Scholar
31. J. M. Renno and B. R. Mace, On the forced response of waveguides using the wave and finite element method, J. Sound Vibr. 329(26) (2010) 5474–5488. Crossref, Web of Science, Google Scholar
32. J.-M. Mencik, On the low-and mid-frequency forced response of elastic structures using wave finite elements with one-dimensional propagation, Comput. Struct. 88(11) (2010) 674–689. Crossref, Web of Science, Google Scholar
33. W. X. Zhong and F. W. Williams, On the direct solution of wave propagation for repetitive structures, J. Sound Vibr. 181(3) (1995) 485–501. Crossref, Web of Science, Google Scholar
34. J.-M. Mencik, A model reduction strategy for computing the forced response of elastic waveguides using the wave finite element method, Comput. Methods Appl. Mech. Eng. 229 (2012) 68–86. Crossref, Web of Science, Google Scholar
35. B. R. Mace and E. Manconi, Wave motion and dispersion phenomena: Veering, locking and strong coupling effects, J. Acoust. Soc. Am. 131(2) (2012) 1015–1028. Crossref, Web of Science, Google Scholar
36. O. Doutres, N. Dauchez, J.-M. Génevaux and O. Dazel, Validity of the limp model for porous materials: A criterion based on the Biot theory, J. Acoust. Soc. Am. 122(4) (2007) 2038–2048. Crossref, Web of Science, Google Scholar
37. D. L. Johnson, J. Koplik and R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, J. Fluid Mech. 176(1) (1987) 379–402. Crossref, Web of Science, Google Scholar
38. Y. Champoux and J.-F. Allard, Dynamic tortuosity and bulk modulus in air-saturated porous media, J. Appl. Phys. 70(4) (1991) 1975–1979. Crossref, Web of Science, Google Scholar
39. D. Rhazi and N. Atalla, Transfer matrix modeling of the vibroacoustic response of multi-materials structures under mechanical excitation, J. Sound Vibr. 329(13) (2010) 2532–2546. Crossref, Web of Science, Google Scholar
40. M. A. Biot and D. G. Willis, The elastic coefficients of the theory of consolidation, J. Appl. Mech. 24 (1957) 594–601. Crossref, Google Scholar