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.
Wochner
Mark S
MS
Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78713-8029, USA.
Hamilton
Mark F
MF
Ilinskii
Yurii A
YA
Zabolotskaya
Evgenia A
EA
D004548:Elasticity; D016014:Linear Models; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D011048:Polarography; D033081:Shear Strength; D014465:Ultrasonics; D014783:Viscosity