``A THREE-DIMENSIONAL DYADIC GREEN'S FUNCTION FOR ELASTIC WAVES IN MULTILAYER CYLINDRICAL STRUCTURES,''

C. C. Lu and Q. H. Liu

The three-dimensional dyadic Green's function for multilayer cylindrical structures is very important for solutions of elastic waves with arbitrary sources in such media. Both the promary and reflected parts of Green's function are expressed as a Fourier integral in z (axial coordinate) and a Fourier series in theta (azimuthal coordinate). In this spectral domain, the reflection matrices can be found recursively by using the boundary conditions at the layer interfaces. Inverse transforming this solution yields the dyadic Green's function in the spatial domain. The Green's function derived and implemented is applicable to arbitrary cylindrically layered media, including three types of interfaces: (i) fluid/solid interfaces, (ii) well-boundedsolid/solid interfaces, and (iii) unbounded solid/solid interfaces. Various numerical results from previous methods for simpler cases and several specially designed simulations validate the numerical implementation. With the Green's function, one can solve for the fields due to an arbitrary source located ar an arbitrary position using the superposition principle. This provides a powerfull tool for the modeling of effects from defects and material inhomogeneities in cylindrical structures.