×

zbMATH — the first resource for mathematics

Poroacoustic acceleration waves. (English) Zbl 1149.74345
Summary: A model for acoustic waves in a porous medium is investigated. Due to the use of lighter materials in modern buildings and noise concerns in the environment, such models for poroacoustic waves are of much interest to the building industry. The model has been investigated in some detail by P. M. Jordan. Here we present a rational continuum thermodynamic derivation of the Jordan model. We then present results for the amplitude of an acceleration wave making no approximations whatsoever.

MSC:
74J10 Bulk waves in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Batchelor, G.K. 1967 An introduction to fluid dynamics. Cambridge, UK: Cambridge University Press. · Zbl 0152.44402
[2] Chen, P.J. 1973 Growth and decay of waves in solids. <i>Handbuch der Physik</i> (eds. Flügge, S. & Truesdell, C.), vol. VIa/3. pp. 303–402, Berlin, Germany: Springer
[3] Christov, C.I. & Jordan, P.M. 2005 Heat conduction paradox involving second sound propagation in moving media. <i>Phys. Rev. Lett.</i>&nbsp;<b>94</b>, 154301-1–154301-4, (doi:10.1103/PhysRevLett.94.154301).
[4] Eringen, A.C. 1994 A continuum theory of swelling porous elastic soils. <i>Int. J. Eng. Sci.</i>&nbsp;<b>32</b>, 1337–1349, (doi:10.1016/0020-7225(94)90042-6).
[5] Fellah, Z.E.A. & Depollier, C. 2000 Transient acoustic wave propagation in rigid porous media: a time-domain approach. <i>J. Acoust. Soc. Am.</i>&nbsp;<b>107</b>, 683–688, (doi:10.1121/1.428250).
[6] Fellah, Z.E.A., Depollier, C., Berger, S., Lauriks, W., Trompette, P. & Chapelon, J.Y. 2003 Determination of transport parameters in air-saturated porous materials via reflected ultrasonic waves. <i>J. Acoust. Soc. Am.</i>&nbsp;<b>114</b>, 2561–2569, (doi:10.1121/1.1621393).
[7] Fu, Y.B. & Scott, N.H. 1988 Acceleration wave propagation in an inhomogeneous heat conducting elastic rod of slowly varying cross section. <i>J. Therm. Stresses</i>&nbsp;<b>15</b>, 253–264.
[8] Fu, Y.B. & Scott, N.H. 1991 The transistion from acceleration wave to shock wave. <i>Int. J. Eng. Sci.</i>&nbsp;<b>29</b>, 617–624, (doi:10.1016/0020-7225(91)90066-C).
[9] Jordan, P.M. 2004 An analytical study of Kuznetsov’s equation: diffusive solitons, shock formation, and solution bifurcation. <i>Phys. Lett. A</i>&nbsp;<b>326</b>, 77–84, (doi:10.1016/j.physleta.2004.03.067). · Zbl 1161.35475
[10] Jordan, P.M. 2005 Growth and decay of acoustic acceleration waves in Darcy-type porous media. <i>Proc. R. Soc. A</i>&nbsp;<b>461</b>, 2749–2766, (doi:10.1098/rspa.2005.1477). · Zbl 1186.76680
[11] Jordan, P.M. & Christov, C.I. 2005 A simple finite difference scheme for modelling the finite-time blow-up of acoustic acceleration waves. <i>J. Sound Vib.</i>&nbsp;<b>281</b>, 1207–1216, (doi:10.1016/j.jsv.2004.03.067). · Zbl 1236.76039
[12] Jordan, P.M. & Feuillade, C. 2004 On the propagation of harmonic acoustic waves in bubbly liquids. <i>Int. J. Eng. Sci.</i>&nbsp;<b>42</b>, 1119–1128, (doi:10.1016/j.ijengsci.2003.12.005). · Zbl 1211.76128
[13] Jordan, P.M. & Puri, A. 1999 Digital signal propagation in dispersive media. <i>J. Appl. Phys.</i>&nbsp;<b>85</b>, 1273–1282, (doi:10.1063/1.369258).
[14] Jordan, P.M. & Puri, A. 2005 Growth/decay of transverse acceleration waves in nonlinear elastic media. <i>Phys. Lett. A</i>&nbsp;<b>341</b>, 427–434, (doi:10.1016/j.physleta.2005.05.010). · Zbl 1171.74321
[15] Jordan, P.M., Meyer, M.R. & Puri, A. 2000 Causal implications of viscous damping in compressible fluid flows. <i>Phys. Rev. E</i>&nbsp;<b>62</b>, 7918–7926, (doi:10.1103/PhysRevE.62.7918).
[16] Maysenhölder, W. Berg, A. & Leistner, P. 2004 Acoustic properties of aluminium foams–measurements and modelling. <i>CFA/DAGA’04</i>, Strasbourg, 22–25/03/2004. See also www.ibp.fhg.de/ba/forschung/aluschaum/aluschaum.pdf. <a target=”_blank” href=’www.ibp.fhg.de/ba/forschung/aluschaum/aluschaum.pdf’>www.ibp.fhg.de/ba/forschung/aluschaum/aluschaum.pdf</a>
[17] Nield, D. & Bejan, A. 1999 Convection in porous media. 2nd edn. New York, NY: Springer. · Zbl 0924.76001
[18] Ostoja-Starzewski, M. & Trebicki, J. 1999 On the growth and decay of acceleration waves in random media. <i>Proc. R. Soc. A</i>&nbsp;<b>455</b>, 2577–2614, (doi:10.1098/rspa.1999.0446). · Zbl 0941.74027
[19] Puri, P. & Jordan, P.M. 2004 On the propagation of plane waves in type-III thermoelastic media. <i>Proc. R. Soc. A</i>&nbsp;<b>460</b>, 3203–3221, (doi:10.1098/rspa.2004.1341). · Zbl 1072.74038
[20] Quintanilla, R. & Straughan, B. 2004 Discontinuity waves in type III thermoelasticity. <i>Proc. R. Soc. A</i>&nbsp;<b>460</b>, 1169–1175, (doi:10.1098/rspa.2003.1131). · Zbl 1070.74024
[21] Su, S., Dai, W., Jordan, P.M. & Mickens, R.E. 2005 Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation. <i>Int. J. Heat Mass Tran.</i>&nbsp;<b>48</b>, 2233–2241, (doi:10.1016/j.ijheatmasstransfer.2004.12.024). · Zbl 1189.80029
[22] Wilson, D.K. 1997 Simple, relaxational models for the acoustic properties of porous media. <i>Appl. Acoust.</i>&nbsp;<b>50</b>, 171–188, (doi:10.1016/S0003-682X(96)00048-5).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.