A COMPUTATIONALLY EFFICIENT REPRESENTATION FOR PROPAGATION OF ELASTIC-WAVES IN ANISOTROPIC SOLIDS

A new closed-form representation is developed for the exact solution of the Christoffel equation for wave propagation in solids. The new representation is numerically more efficient than the traditional representations based on the use of Fourier and Laplace transforms. Using the new representation, the retarded Green's functions are derived for an infinite anisotropic solid and an anisotropic half-space. The method is applied to calculate the elastic-wave response of an anisotropic cubic solid to highly localized delta function and step function type impulses. Both surface and bulk wave responses have been calculated. The effect of anisotropy is discussed by considering cubic solids with different anisotropy parameters. Interestingly, it is found that, for certain values of the anisotropy parameter, two distinct longitudinally polarized components can be observed to propagate along an axis of cubic symmetry. One of the signals is the normal longitudinal wave signal while the other results from the concave shape of the transverse slowness surface.