Cubic nonlinearity in shear wave beams with different polarizations

Journal of the Acoustical Society of America

Volumn 123, Issue 5, 2008, Pages 2488-2495

  Wochner, Mark S ^a   Hamilton, Mark F ^a   Ilinskii, Yurii A ^a   Zabolotskaya, Evgenia A ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTROMAGNETIC WAVE POLARIZATION; EQUATIONS OF MOTION; SHEAR WAVES;

COMPRESSIONAL WAVE BEAMS; CUBIC NONLINEARITY; ISOTROPIC ELASTIC;

NONLINEAR EQUATIONS;

ARTICLE; MATHEMATICAL MODEL; NONLINEAR SYSTEM; POLARIZATION; PRIORITY JOURNAL; SHEAR RATE; WAVEFORM;

ELASTICITY; LINEAR MODELS; MODELS, THEORETICAL; NONLINEAR DYNAMICS; POLAROGRAPHY; SHEAR STRENGTH; ULTRASONICS; VISCOSITY;

EID: 43549087864     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.2890739     Document Type: Article

References (17)

1. E. A. Zabolotskaya, " Sound beams in a nonlinear isotropic solid., " Sov. Phys. Acoust. 32, 296-299 (1986).
2. I. P. Lee-Bapty and D. G. Crighton, " Nonlinear wave motion governed by the modified Burgers equation., " Philos. Trans. R. Soc. London, Ser. A 323, 173-209 (1987).
3. O. V. Rudenko and O. A. Sapozhnikov, " Wave beams in cubically nonlinear nondispersive media., " J. Exp. Theor. Phys. 79, 220-229 (1994).
4. O. V. Rudenko and O. A. Sapozhnikov, " Self-action effects for wave beams containing shock fronts., " Phys. Usp. 47, 907-922 (2004).
5. S. Catheline, J.-L. Gennisson, M. Tanter, and M. Fink, " Observation of shock transverse waves in elastic media., " Phys. Rev. Lett. 91, 164301 (2003).
6. S. Catheline, J.-L. Gennisson, and M. Fink, " Measurement of elastic nonlinearity of soft solid with transient elastography., " J. Acoust. Soc. Am. 114, 3087-3091 (2003).
7. M. F. Hamilton, Yu. A. Ilinskii, and E. A. Zabolotskaya, " Separation of compressibility and shear deformation in the elastic energy density., " J. Acoust. Soc. Am. 116, 41-44 (2004).
8. E. A. Zabolotskaya, M. F. Hamilton, Yu. A. Ilinskii, and G. D. Meegan, " Modeling of nonlinear shear waves in soft solids., " J. Acoust. Soc. Am. 116, 2807-2813 (2004).
9. M. S. Wochner, M. F. Hamilton, Yu. A. Ilinskii, and E. A. Zabolotskaya, " Nonlinear shear wave beams in soft tissue-like media., " Proceedings of the 19th International Congress on Acoustics, Madrid, Spain, 2-7 September 2007, Paper No. NLA-03-003-IP.
10. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd ed. (Pergamon, New York, 1986).
11. Z. A. Gol'dberg, " Interaction of plane longitudinal and transverse elastic waves., " Sov. Phys. Acoust. 6, 306-310 (1961).
12. B. O. Enfio, C. M. Hedberg, and O. V. Rudenko, " Wave motion in a medium with a cubic nonlinearity., " Proceedings of the Fourth Polyakov Readings, St. Petersburg, Russia, 7-10 February 2006, pp. 65-74.
13. S. Kostek, B. K. Sinha, and A. N. Norris, " Third-order elastic constants for an inviscid fluid., " J. Acoust. Soc. Am. 94, 3014-3017 (1993).
14. Nonlinear Acoustics, edited by, M. F. Hamilton, and, D. T. Blackstock, (Academic, New York, 1998).
15. G. Fibich and B. Ilan, " Self-focusing of circularly polarized beams., " Phys. Rev. E 67, 036622 (2003).
16. Y.-S. Lee and M. F. Hamilton, " Time-domain modeling of pulsed finite-amplitude sound beams., " J. Acoust. Soc. Am. 97, 906-917 (1995).
17. C.-W. Shu, " Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws., " in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture Notes in Mathematics Vol. 1697, edited by, A. Quarteroni, (Springer, Berlin, 1998), pp. 325-432.