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Dynamic effective mass of granular media and the attenuation of structure-borne sound
Phys. Rev. E 80, 051304 – Published 30 November, 2009
DOI: https://doi.org/10.1103/PhysRevE.80.051304
Abstract
We report a theoretical and experimental investigation into the fundamental physics of why loose granular media are effective deadeners of structure-borne sound. Here, we demonstrate that a measurement of the effective mass, , of the granular medium is a sensitive and direct way to answer the question: what is the specific mechanism whereby acoustic energy is transformed into heat? Specifically, we apply this understanding to the case of the flexural resonances of a rectangular bar with a grain-filled cavity within it. The pore space in the granular medium is air of varying humidity. The dominant features of are a sharp resonance and a broad background, which we analyze within the context of simple models. We find that: (a) on a fundamental level, dampening of acoustic modes is dominated by adsorbed films of water at grain-grain contacts, not by global viscous dampening or by attenuation within the grains. (b) These systems may be understood, qualitatively, in terms of a height-dependent and diameter-dependent effective sound speed and an effective viscosity . (c) There is an acoustic Janssen effect in the sense that, at any frequency, and depending on the method of sample preparation, approximately one-half of the effective mass is borne by the side walls of the cavity and one-half by the bottom. (d) There is a monotonically increasing effect of humidity on the dampening of the fundamental resonance within the granular medium which translates to a nonmonotonic, but predictable, variation in dampening within the grain-loaded bar.
Corrections
3 December, 2009
Erratum
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References (40)
- W. Kuhl and H. Kaiser, Acustica 2, 179 (1962).
- L. Cremer and M. Heckl, Structure Borne Sound (Springer, Berlin, 1973).
- J. M. Bourinet and D. Le Houèdec, Comput. Struct. 73, 395 (1999).
- J. M. Bourinet and D. Le Houèdec, in Powders & Grains 97, edited by R. Behringer and J. Jenkins (Balkema, Rotterdam, 1997).
- G. Kurtze, VDI-Berichte 8, 110 (1956).
- C.-J. Hsu, D. L. Johnson, R. A. Ingale, J. J. Valenza, N. Gland, and H. A. Makse, Phys. Rev. Lett. 102, 058001 (2009).
- J. C. Sun, H. B. Sun, L. C. Chow, and E. J. Richards, J. Sound Vib. 104, 243 (1986).
- S. A. Nayfeh, J. M. Verdirame, and K. K. Varanasi, Proc. SPIE 4697, 158 (2002).
- K. K. Varanasi and S. A. Nayfeh, Proceedings of the DETC’03 ASME Design Eng. Technical Conference, 2003 (unpublished).
- W. Kang, J. A. Turner, F. Bobaru, L. Yang, and K. Rattanadit, J. Acoust. Soc. Am. 121, 888 (2007).
- B. R. Tittmann, V. A. Clark, and J. M. Richardson, J. Geophys. Res. 85, 5199 (1980).
- Th. Brunet, X. Jia, and P. Mills, Phys. Rev. Lett. 101, 138001 (2008).
- L. E. Kinsler and A. E. Frey, Fundamentals of Acoustics (Wiley, New York, 1950).
- J. B. Mehl, J. Acoust. Soc. Am. 64, 1523 (1978); M. B. Ewing and J. P. M. Trusler, ibid. 85, 1780 (1989).
- W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (Cambridge University Press, New York, 1987).
- J. B. Knight, C. G. Fandrich, C. N. Lau, H. M. Jaeger, and S. R. Nagel, Phys. Rev. E 51, 3957 (1995); E. R. Nowak, J. B. Knight, M. L. Povinelli, H. M. Jaeger, and S. R. Nagel, Powder Technol. 94, 79 (1997); E. R. Nowak, J. B. Knight, E. Ben-Naim, H. M. Jaeger, and S. R. Nagel, Phys. Rev. E 57, 1971 (1998); J. Brujić, P. Wang, C. Song, D. L. Johnson, O. Sindt, and H. A. Makse, Phys. Rev. Lett. 95, 128001 (2005).
- L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960); L. D. Landau and E. M. Lifshitz,Statistical Physics, 2nd ed. (Addison-Wesley, Reading, MA, 1969).
- L. D. Landau and E. M. Lifshitz, Fluid Dynamics (Pergamon, New York, 1978).
- D. L. Johnson and P. N. Sen, Phys. Rev. B 24, 2486 (1981); D. L. Johnson, J. Koplik, and R. Dashen, J. Fluid Mech. 176, 379 (1987).
- M. J. Turner, I. M. MacLeod, and A. D. Rothberg, J. Appl. Physiol. 67, 472 (1989).
- A. Selfridge, IEEE Trans. Sonics Ultrason. SU-32, 381 (1985).
- G. Becker, Handbook of Chemistry and Physics, 81st ed. (CRC Press, Cleveland, 2000).
- C. H. Liu and S. R. Nagel, Phys. Rev. Lett. 68, 2301 (1992); Phys. Rev. B 48, 15646 (1993).
- F. D. Shields, J. M. Sabatier, and M. Wang, J. Acoust. Soc. Am. 108, 1998 (2000).
- H. Schmidt, Acustica 4, 639 (1954).
- Y. Bertho, F. Giorgiutti-Dauphine, and J.-P. Hulin, Phys. Rev. Lett. 90, 144301 (2003).
- H. A. Makse, N. Gland, D. L. Johnson, and L. M. Schwartz, Phys. Rev. E 70, 061302 (2004).
- N. V. Brilliantov, F. Spahn, J.-M. Hertzsch, and T. Pöschel, Phys. Rev. E 53, 5382 (1996).
- J. Schäfer, S. Dippel, and D. E. Wolf, J. Phys. I (France) 6, 5 (1996).
- J. Crassous, E. Charlaix, and J.-L. Loubet, Phys. Rev. Lett. 78, 2425 (1997).
- J. Crassous, E. Charlaix, H. Gayvallet, and J.-L. Loubet, Langmuir 9, 1995 (1993).
- L. Rayleigh, Theory of Sound (Dover, New York, 1945).
- C. Thornton and D. J. Barnes, Acta Mech. 64, 45 (1986).
- R. J. O’Connell and B. Budiansky, J. Geophys. Res. 79, 5412 (1974).
- J. N. D’Amour, J. J. R. Stålgren, K. K. Kanazawa, C. W. Frank, M. Rodahl, and D. Johannsmann, Phys. Rev. Lett. 96, 058301 (2006).
- S. Timoshenko and D. H. Young, Vibration Problems in Engineering, 3rd ed. (Van Nostrand, Princeton, New York, 1955).
- J. Valenza, C.-J. Hsu, and D. L. Johnson (unpublished).
- S. J. Gregg and K. S. W. Sing, Adsorption, Surface Area and Porosity, 2nd ed. (Academic, New York, 1982).
- W. M. Murphy, K. W. Winkler, and R. L. Kleinberg, Geophysics 51, 757 (1986).
- A. N. Norris and D. L. Johnson, ASME J. Appl. Mech. 64, 39 (1997).