Cubic nonlinearity in shear wave beams with different polarizations.
A coupled pair of nonlinear parabolic equations is derived for the two components of the particle motion perpendicular to the axis of a shear wave beam in an isotropic elastic medium. The equations account for both quadratic and cubic nonlinearity. The present paper investigates, analytically and numerically, effects of cubic nonlinearity in shear wave beams for several polarizations: linear, elliptical, circular, and azimuthal. Comparisons are made with effects of quadratic nonlinearity in compressional wave beams.
Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78713-8029, USA.
Mark S
MS
Wochner
Mark F
MF
Hamilton
Yurii A
YA
Ilinskii
Evgenia A
EA
Zabolotskaya
D004548:Elasticity; D016014:Linear Models; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D011048:Polarography; D033081:Shear Strength; D014465:Ultrasonics; D014783:Viscosity