Scattering of Elastic Waves by Inhomogeneities in Cylindrical Structures
In the present thesis we extend the null field approach (in the literature also often referred to as "the T matrix method" or "the extended boundary condition method") to some new multiple scattering problems involving infinite cylindrical surfaces and a bounded obstacle. The first case considered is the scattering of acoustic waves by a bounded obstacle outside an infinite cylinder of constant cross section. The incident wave is chosen as a plane wave and we apply sound-hard boundary conditions. An elastic infinite circular cylinder with an embedded obstacle is the configuration investigated next. Here the boundary conditions are those of vanishing surface tractions and both the case of guided modes and when the cylinder is excited by a point force, applied perpendicularly to its surface, are considered. This geometry is then further extended by adding an additional cylindrical surface, thus yielding a cylindrical pipe with an embedded obstacle. Also in this case we apply vanishing surface traction to the boundaries involved and we excite the pipe by applying a point force on its outer cylindrical surface. In all cases the scattered field is obtained as an expression containing the transition matrix for the obstacle, the reflection matrices for the participating cylindrical surfaces, the transformation function between the cylindrical and spherical basis functions and, for the cases when it is utilized in the derivation, the translation function for the cylindrical waves. Specializing, in all cases, to circular cylindrical surfaces and spherical (or penny-shaped) obstacles, numerical computations have been carried out in the low and intermediate frequency regions. Results are presented for various quantities of interest such as cross sections, far field amplitudes, displacements and energy transmission and reflection coefficients.