Summary
Acoustic radiation from a finite spherical source, vibrating with an arbitrary, axisymmetric, time-harmonic surface velocity distribution, while immersed at an arbitrary point near a poroelastic sphere in an unbounded ideal fluid medium is analyzed in an exact manner. The formulation utilizes the appropriate wave-field expansions, along with the translational addition theorems for spherical wave functions in combination with the Biot classic model for the description of poroelastic material behavior, to develop a closed-form solution in form of infinite series. The prime objective is to investigate the dynamic poroelasticity effects on acoustic radiation and its associated field quantities. The analytical results are illustrated with a numerical example, in which the spherical source, excited in vibrational modes of zero-th or first order, is positioned near a water-saturated sandstone sphere. The basic acoustic field quantities such as the modal acoustic radiation impedance load on the source, the radiated far-field pressure directivity pattern, and the radial acoustic intensity distribution are evaluated and discussed for representative values of the parameters characterizing the system.
Similar content being viewed by others
References
Karnovskii, M. I.: Interaction acoustical impedance of spherical radiators and resonators. CR (Dokl) Acad Sci URSS 32 (1941) 40–43
Ingard, U., Lamb, Jr. G. L.: Effect of a reflecting plane on the output of sound sources. J. Acoust. Soc. Am. 29 (1957) 743–744.
New, R., Eisler, T. J.: Acoustic radiation from multiple spheres. J. Sound. Vib. 22 (1972) 1–17
Ivanov, Y. A.: Diffraction of electromagnetic waves on two bodies. NASA Technical Translation F-597, National Aeronautics and Space Administration, Washington DC 1970
Thompson, Jr. W.: Radiation from a spherical acoustic source near a scattering sphere. J Acoust Soc Am 60 (1976) 781–787
Thompson, Jr. W.: Acoustic coupling between two finite-sized spherical sources. J Acoust Soc Am 62 (1977) 8–11
Thompson, Jr. W.: Acoustic coupling between a pulsating and an oscillating sphere. J Acoust Soc Am 74 (1983) 1050–1148
Thompson, Jr. W.: Acoustic radiation from a spherical source embedded eccentrically within a fluid sphere. J Acoust Soc Am 54 (1973) 1694–1707
Lease, A., Thompson, Jr. W.: Use of translational addition theorems for spherical wave functions in nonaxisymmetric acoustic field problems. J Acoust Soc Am 90 (1991) 1155–1160
Lease, A., Thompson, Jr. W.: Nonaxisymmetric acoustic radiation from a pair of sources embedded in a fluid sphere. J Acoust Soc Am 90 (1991) 1161–1166
Hasheminejad, S. M., Azarpeyvand, M.: Eccentricity effects on acoustic radiation from a spherical source suspended within a thermoviscous fluid sphere. IEEE Trans Ultrason Ferroelect Freq Contr 50 (2003) 1444–1454
Gassmann, F.: Uber die Elastizitat poröser Medien. Viereljahreschrift d. Naturforsch. Gesell. Zurich 96 (1951) 1–23
Biot, M. A.: Mechanics of deformation and acoustic propagation in porous media. J Appl Phys 23 (1962) 1482–1498
Gurevich, B., Kelder, O., Smeulders, D. M. J.: Validation of the slow compressional wave in porous media: Comparison of experiments and numerical simulations. Transport Porous Media 36 (1999) 149–160
Auriault, J. L., Geindreau, C., Royer, P., Block, J. F.: Proceedings of the 2nd Biot Conference on Poromechanics. Grenoble France 2002
Pierce, A. D.: Acoustics: An introduction to its physical principles and applications. American Inst Physics, New York 1991
Abramowitz, M., Stegun, I. A.: Handbook of mathematical functions. National Bureau of Standards, Washington, DC 1964
Bourbie, T., Coussy, O., Zinszner, B. E.: Acoustics of porous media. Gulf Publishing, Houston 1987
Allard, J. F.: Propagation of sound in porous media: modelling sound absorbing materials. Elsevier Applied Science, London 1993
Johnson, D. L., Koplik, J., Dashen, R.: Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J Fluid Mech 76 (1987) 379–402
Achenbach, J. D.: Wave propagation in elastic solids. North-Holland, New York 1976
Deresiewicz, H., Skalak, R.: On uniqueness in dynamic poroelasticity. Bull Seismol Soc Am 53 (1963) 783–788
Hasheminejad, S. M., Hosseini, H.: Radiation loading of a cylindrical source in a fluid-filled cylindrical cavity embedded within a fluid-saturated poroelastic medium. J Appl Mech 69 (2002) 675–683
Junger, M. C., Feit, D.: Sound structures and their interaction, 2nd edn. MIT Press, Cambridge 1986
Johnson, D. L., Plona, T. J., Kojima, H.: Probing proous media with first and second sound, II: acoustic properties of water-saturated porous media. J Appl Phys 76 (1994) 115–125.
Dukhin, A. S., Goetz, P. J., Simmons, D. H. M.: Ultrasound for characterizing colloids. Elsevier Health Sciences, London, pp 166–168 (2002)
Riebel, U.: Characterization of agglomerates and porous particles by ultrasonic spectrometry. Vortrag Partec, Nürnberg, Preprints 2, pp 545–559 (1992)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hasheminejad, S.M., Mehdizadeh, S. Acoustic radiation from a finite spherical source placed in fluid near a poroelastic sphere. Arch. Appl. Mech. 74, 59–74 (2004). https://doi.org/10.1007/BF02637209
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02637209