On nonlinearity parameters describing elastic wave interactions

Abstract

Elastic wave interaction coefficients were defined in the case of arbitrary n-th order nonlinearity and calculated explicitly in cases of quadratically and cubically nonlinear interactions. In the first case the isotropic Murnaghan material, and the cubic crystal of class m3m were analyzed. The calculated coefficients were displayed graphically in the form of tables which reveal the difference in behavior of shear elastic waves for isotropic and anisotropic materials. In the isotropic case there is no quadratically nonlinear coupling between propagating collinearly shear waves and the appropriate coefficients disappear. In the anisotropic case there are special directions along which such a coupling takes place and the coefficients responsible for this coupling are not equal to zero. Moreover, choosing a particular direction of propagation, namely a three-fold symmetry acoustic axis, (e.g. [111] direction in a cubic crystal) results in a a very special symmetry among these coefficients. Besides, the cubically nonlinear interaction coefficients were calculated for a model of a soft solid.Elastic wave interaction coefficients were defined in the case of arbitrary n-th order nonlinearity and calculated explicitly in cases of quadratically and cubically nonlinear interactions. In the first case the isotropic Murnaghan material, and the cubic crystal of class m3m were analyzed. The calculated coefficients were displayed graphically in the form of tables which reveal the difference in behavior of shear elastic waves for isotropic and anisotropic materials. In the isotropic case there is no quadratically nonlinear coupling between propagating collinearly shear waves and the appropriate coefficients disappear. In the anisotropic case there are special directions along which such a coupling takes place and the coefficients responsible for this coupling are not equal to zero. Moreover, choosing a particular direction of propagation, namely a three-fold symmetry acoustic axis, (e.g. [111] direction in a cubic crystal) results in a a very special symmetry among these coefficients. Besides, the cubic...