Propagation of radially polarized shear wave beams with cubic and quadratic nonlinearities.

Abstract

This presentation describes an extension of the work by Wochner et al. [J. Acoust. Soc. Am. 123, 2488–2495 (2008)], wherein a coupled pair of nonlinear parabolic equations was derived for the two components of the particle motion perpendicular to the axis of a shear wave beam in an isotropic hyperelastic medium. Although the equations derived in that work contain both cubic and quadratic nonlinearities, the latter were discarded based on the fact that they are not present in plane shear waves, and hence assumed negligible within the quasiplane paraxial region of linearly polarized shear wave beams. However, the experimental observation of prominent second harmonic generation by nonplanar shear waves in soft solids [Jacob et al., J. Acoust. Soc. Am. 122, 1917–1926 (2007)] has motivated a more thorough understanding of these quadratic nonlinear terms. In the present work, the quadratic nonlinearity is explored, and, in particular, it is found that the form of this nonlinearity simplifies for axisymmetric radially polarized beams. Numerical results are presented comparing the effects of the cubic and quadratic nonlinearities on the generation of harmonics along the beam axis and the directivity patterns of those harmonics. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.]