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Acoustic modeling of light and non-cohesive poro-granular materials with a fluid/fluid model

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Summary

Poro-granular materials are studied, and a model adapted to characterize their acoustic behaviour is presented. Biot’s theory is used to obtain this model but a great simplification is brought to classical formulation. Indeed, a solid phase being made of a non-cohesive poro-granular material, a specific continuum constitutive model is used to characterize its behaviour. The macroscopic coefficient of friction that takes into account friction and collision phenomena is then neglected under specific conditions. This strong assumption does not apply for all kinds of granular materials and for any solicitations: its validity is discussed for particular materials. The solid/fluid model of Biot’s theory is then transformed to an equivalent fluid/fluid model. The complexity of the classical formulation is significantly reduced since only two degrees of freedom are used: the solid and fluid pressures. A 1D case is then treated to present the simplicity of the formulation, and applied to a poro-granular material made of expanded polystyrene beads. Intrinsic parameters of this material are adjusted thanks to surface impedances measured with a stationary waves tube. Finally, a study on thermal and viscous dissipations is realized and associated with a study on pressure and velocity distribution in the sample.

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References

  1. Zwikker C. and Kosten C.W. (1949). Sound-Absorbing Materials. Elsevier, New York

    Google Scholar 

  2. Attenborough K. (1983). Acoustical characteristics of rigid fibrous absorbents and granular media. J. Acoust. Soc. Am. 73: 785–799

    Article  MATH  Google Scholar 

  3. Delany, M.E., Bazley, E.N.: Acoustical properties of fibrous asorbent materials. Appl. Acoust. 3 (1970)

  4. Champoux Y. and Allard J.-F. (1991). Dynamic tortuosity and bulk modulus in air-saturated porous media. J. Appl. Phys. 70: 1975–1979

    Article  Google Scholar 

  5. Johnson D.L., Plona T.J. and Scala C. (1982). Tortuosity and acoustic slow waves. Phys. Rev. Lett. 49: 1840–1844

    Article  Google Scholar 

  6. Stinson M.R. and Champoux Y. (1992). Propagation of sound and the assignment of shape factors in model porous materials having simple pore geometries. J. Acoust. Soc. Am. 91: 685–695

    Article  Google Scholar 

  7. Lafarge D., Lemarinier P., Allard J.F. and Tarnow V. (1997). Dynamic compressibility of air in porous structures at audible frequencies. J. Acoust. Soc. Am. 102: 1995–2006

    Article  Google Scholar 

  8. Allard J.F. (1993). Propagation of Sound in Porous Media, Modeling Sound Absorbing Materials. Elsevier, London

    Google Scholar 

  9. Biot M.A. (1956). The theory of propagation of elastic waves in a fluid saturated porous solid –I. Low-frequency range. J. Acoust. Soc. Am. 28: 168–178

    Article  MathSciNet  Google Scholar 

  10. Biot M.A. (1956). The theory of propagation of elastic waves in a fluid saturated porous solid–II. Higher frequency range. J. Acoust. Soc. Am. 28: 178–191

    Google Scholar 

  11. Biot M.A. (1962). Generalized theory of acoustic propagation in porous dissipative media. J. Acoust. Soc. Am. 34: 1254–1264

    Article  MathSciNet  Google Scholar 

  12. Biot M.A. (1956). The theory of propagation of elastic waves in a fluid saturated porous solid. J. Acoust. Soc. Am. 28: 168–191

    Article  MathSciNet  Google Scholar 

  13. Lauriks, W., Boeckx, L., Leclaire, P., Khurana, P., Kelders, L.: Characterisation of porous acoustic materials. In: SAPEM Proceedings, ENTPE Lyon (2005)

  14. Fellah Z.E.A., Fellah M., Sebaa N., Lauriks W. and Depollier C. (2006). Measuring flow resistivity of porous materials at low frequencies range via acoustic transmitted waves (l). J. Acoust. Soc. Am. 119: 1926–1928

    Article  Google Scholar 

  15. Perrot, C., Panneton, R., Olny, X.: Computation of the dynamic bulk modulus of acoustic foams. In: SAPEM, ENTPE Lyon (2005)

  16. Iannace, G., Ianiello, C., Maffei, L., Romano, R.: Characteristic impedance and complex wave-number of limestone chips. In: 4th European Conference on Noise Control, Euronoise (2001)

  17. Courtois, T., Falk, T., Bertolini, C.: An acoustical inverse measurement system to determine intrinsic parameters of porous samples. In: SAPEM, ENTPE Lyon (2005)

  18. Dragonetti R., Ianniello C. and Romano R. (2004). The use of an optimization tool to search non-acoustic parameters of porous materials. Inter-noise, Prague

    Google Scholar 

  19. Allard J.F., Depollier C., Rebillard P., Lauriks W. and Cops A. (1989). Inhomogeneous Biot waves in layered media. J. Appl. Phys. 66: 2278–2284

    Article  Google Scholar 

  20. Atalla, N.: An overview of the numerical modeling of poroelastic materials. In: SAPEM, ENTPE Lyon (2005)

  21. Panneton R. and Atalla N. (1997). An efficient finite element scheme for solving the three dimensional poroelasticity problem in acoustics. J. Acoust. Soc. Am. 101: 3287–3298

    Article  Google Scholar 

  22. Atalla N., Panneton R. and Debergue P. (1998). A mixed displacement–pressure formulation for poroelastic materials. J. Acoust. Soc. Am. 104: 1444–1452

    Article  Google Scholar 

  23. Atalla N., Hamdi M.A. and Panneton R. (2001). Enhanced weak integral formulation for the mixed (u, p) poroelastic equations. J. Acoust. Soc. Am. 109: 3065–3068

    Article  Google Scholar 

  24. Debergue P., Panneton R. and Atalla N. (1999). Boundary conditions for the weak formulation of the mixed (u,p) poroelasticity problem. J. Acoust. Soc. Am. 106: 2383–2390

    Article  Google Scholar 

  25. Castel, F.: Example of meshing rule for finite element modelling of simple and double porosity materials. In: SAPEM, ENTPE Lyon (2005)

  26. Dazel O., Sgard F., Lamarque C.-H. and Atalla N. (2002). An extension of complex modes for the resolution of finite-element poroelastic problems. J. Sound Vib. 253: 421–445

    Article  Google Scholar 

  27. Dazel, O., Brouard, B., Depollier, C., Griffiths, S.: An alternative Biot’s displacement formulation for porous materials. J. Acoust. Soc. Am. 121 (2007)

  28. Hamdi, M.A., Zhang, C., Mebarek, L., Anciant, M., Mahieux, B.: Engineering feedback on numerical simulation of fully trimmed vehicles using modified biot’s theory. In: SAPEM, ENTPE, Vaulx en Velin (2005)

  29. Doutres O., Dauchez N., Génevaux J.M. and Dazel O. (2007). Validity of the limp model for porous materials: A criterion based on the Biot theory. J. Acoust. Soc. Am. 122: 2038–2048

    Article  Google Scholar 

  30. Bourinet, J.M.: Approche numérique et expérimentale des vibrations amorties de tubes remplis de matériaux granulaires. Thèse, École Centrale de Nantes (1996)

  31. Bourinet J.M. and Houédec D. (1999). A dynamic stiffness analysis of damped tubes filled with granulars materials. Comput. Struct. 73: 395–406

    Article  MATH  Google Scholar 

  32. Saeki M. (2002). Impact damping with granular materials in a horizontally vibrating system. J. Sound Vib. 251: 153–161

    Article  Google Scholar 

  33. Mao, K., Wang, M.Y., Xu, Z., Chen, T.: Simulation and characterization of particle damping in transient vibrations. American Society of Mechanical Engineers – J. Vib. Acoust. 126 (2004)

  34. Saad M.H., Adhikari G. and Cardoso F. (2000). Dem simulation of wave propagation in granular media. Powder Technol. 109: 222–233

    Article  Google Scholar 

  35. Jia, X., Mills, P.: Sound propagation in dense granular materials. Powders and Grains, Kishino (2001)

  36. Voronina N.N. and Horoshenkov K.V. (2003). A new empirical model for the acoustic properties of loose granular media. Appl. Acoust. 64: 415–432

    Article  Google Scholar 

  37. Attenborough, K.: On the acoustic slow wave in air-filled granular media. J. Acoust. Soc. Am. 81 (1987)

  38. Park, J.: Measurements of the frame acoustic properties of porous and granular materials. J. Acoust. Soc. Am. 118 (2005)

  39. Horoshenkov, K.V., Swift, M.J.: The acoustic properties of granular materials with pore size distribution close to log-normal. J. Acoust. Soc. Am. 110, Pt. 1 (2001)

    Google Scholar 

  40. Allard J.F., Henry M., Tizianel J., Kelders L. and Lauriks W. (1998). Sound propagation in air-saturated random packings of beads. J. Acoust. Soc. Am. 102: 2004–2007

    Article  Google Scholar 

  41. Umnova, O., Attenborough, K., Li, K.M.: Cell model calculations of dynamic drag parameters in packings of spheres. J. Acoust. Soc. Am. 107 (2000)

  42. Gasser, S., Paun, F., Bréchet, Y.: Absorptive properties of rigid porous media: Application to face centered cubic sphere packing. J. Acoust. Soc. Am. 117, Pt. 1 (2005)

    Google Scholar 

  43. Coste C. and Gilles B. (1999). On the validity of Hertz contact law for granular material acoustics. Eur. Phys. J. B 7: 155–168

    Article  Google Scholar 

  44. Daniel R.C., Poloski A.P. and Sáez A.E. (2007). A continuum constitutive model for cohesionless granular flows. Chem. Engng Sci. 62: 1343–1350

    Article  Google Scholar 

  45. Jop P., Forterre Y. and Pouliquen O. (2006). A constitutive law for dense granular flows. Nature 441: 727–731

    Article  Google Scholar 

  46. Schultz T., Shaplak M. and Cattafesta L.N. (2007). Uncertainty analysis of the two microphone method. J. Sound Vib. 304: 91–109

    Article  Google Scholar 

  47. Bodén H. and Abom M. (1985). Influence of errors on the two-microphone method for measuring acoustic properties in ducts. J. Acoust. Soc. Am. 79: 541–549

    Article  Google Scholar 

  48. Seybert A.F. and Soenarko B. (1981). Error analysis of spectral estimates with application to measurement of acoustic parameters using random sound fields in ducts. J. Acoust. Soc. Am. 69: 1190–1199

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Laboratoire Roberval, Centre de Recherches de Royallieu, Université de Technologie de Compiègne, BP 20529, 60205, Compiègne Cedex, France

    J.-D. Chazot

  2. INSA de Lyon, Laboratoire Vibrations Acoustique, Antoine de Saint Exupery, Villeurbanne, France

    J.-L. Guyader

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  1. J.-D. Chazot
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  2. J.-L. Guyader
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Correspondence to J.-D. Chazot.

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Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday

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Chazot, JD., Guyader, JL. Acoustic modeling of light and non-cohesive poro-granular materials with a fluid/fluid model. Acta Mech 195, 227–247 (2008). https://doi.org/10.1007/s00707-007-0571-4

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  • DOI: https://doi.org/10.1007/s00707-007-0571-4

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