A new method to obtain 3-D Green's functions for anisotropic solids

Three-dimensional time-domain elastodynamic basic singular solutions for anisotropic solids have been obtained in relatively simple form by the use of the Radon transform. The procedure is introduced by an application to the simple case of the 3-D scalar wave equation. For general anisotropic solids the Radon transform reduces the set of 3-D hyperbolic partial differential equations to a set of 1-D hyperbolic pde's. The 1-D equations are solved by an eigenvalue decomposition, and the 3-D solution is subsequently expressed as an inversion integral, in the form of an integral over a unit sphere. For general anisotropic materials the integral can be evaluated numerically in a relatively simple manner. Radiated fields are presented for transversely isotropic materials such as ice and graphite epoxy fiber-reinforced composites.