Mode Conversion and Resonance Scattering of Elastic Waves from a Cylindrical, Fluid-Filled Cavity.

Mode conversion and scattering of compressional and shear waves from cylindrical cavities are studied by performing partial wave expansions of the incident and scattered fields. A mathematical analysis, supported by extensive numerical calculations, shows that each partial wave spectrum consists of a smooth background identical to that of an empty cavity and a series of resonance terms associated with the eigenvibrations of the cavity's fluid interior. Resonance scattering of elastic waves is shown to occur when circumferential waves are excited in the fluid interior of the cavity. The resonances which appear in successive normal modes of vibration of the cavity are related through a common feature of the scattering amplitude known in modern physics as a Regge pole. The scattering matrix for the cavity is defined and its unitary and symmetry properties are discussed. Argand diagrams of the trajectories of the S-matrix elements in the complex plane are shown to have certain easily recognized features which are associated with the cavity resonances. The theory is applied to the calculation of the scattering cross-section of the cavity for time-harmonic elastic waves. Using the unitary property of the scattering matrix, expressions for the total scattering cross-sections are obtained which closely resemble the Optical Theorem of modern physics.