Effective medium method for sound propagation in a soft medium containing air bubbles
- 1 September 2008
- journal article
- research article
- Published by Acoustical Society of America (ASA) in The Journal of the Acoustical Society of America
- Vol. 124 (3), 1419-1429
- https://doi.org/10.1121/1.2957931
Abstract
An effective medium method (EMM) is developed to investigate the nonlinear propagation of acoustic waves for soft media containing air bubbles, which accounts for the effects of weak compressibility, viscosity, surrounding pressure, surface tension, and encapsulating shells. Based on the dynamics model of an individual bubble that has included these effects, the EMM is presented by employing a simple perturbation approach to “homogenize” the bubbly soft media. The equations describing the fundamental and the second harmonic waves are derived that applies to three-dimensional cases, and then solved in a one-dimensional case to obtain the effective acoustical parameters of a longitudinal wave. The EMM is compared with the previous theories in three representative cases regarded as simple models of significant practical applications. The results show that the EMM agrees well with the previous theories and can incorporate the additional effects, which may notably affect the accuracy of the results. The limitations of the EMM are also identified and stated.Keywords
This publication has 19 references indexed in Scilit:
- Acoustic localization in weakly compressible elastic media containing random air bubblesPhysical Review E, 2007
- Modifications of the equation for gas bubble dynamics in a soft elastic mediumThe Journal of the Acoustical Society of America, 2005
- Nonlinear dynamics of a gas bubble in an incompressible elastic mediumThe Journal of the Acoustical Society of America, 2004
- Wave propagation in a viscoelastic medium containing fluid-filled microspheresThe Journal of the Acoustical Society of America, 1999
- Wave processes in media with strong acoustic nonlinearityThe Journal of the Acoustical Society of America, 1991
- Comparison of effective medium theories for inhomogeneous continuaThe Journal of the Acoustical Society of America, 1989
- Matrix viscosity and cavity-size distribution effects on the dynamic effective properties of perforated elastomersThe Journal of the Acoustical Society of America, 1984
- Resonance theory of the effective properties of perforated solidsThe Journal of the Acoustical Society of America, 1982
- Multiple Scattering of WavesJournal of Mathematical Physics, 1961
- Pulsation Oscillations of Cavities in RubberThe Journal of the Acoustical Society of America, 1958