Novel formalism for resonance scattering of acoustic and elastic waves

Abstract

A novel formalism for the isolation of resonances from Rayleigh normal modes (or partial waves) of scattered waves for acoustic and elastic wave scattering problems is proposed. The resonance scattering functions consisting purely of resonance information of the scatterer are newly defined. Previous method based on resonance scattering theory, which has been used to extract the vibrational resonance information of the scatterer during last two decades, calculates reasonable magnitude information of the resonances. However, the phases of the resonances extracted by resonance scattering theory show physically unexplainable behavior although it is well known that the phase of a resonance term should shift by radians as the frequency passes through the resonance frequency. And the importance of the phase has been overlooked by previous works. Motivated by this fact, this paper attempts to revisit and review the derivation of the classical resonance scattering theory and develop a new method to extract the resonance information with physically meaningful phases as well as magnitudes. For acoustic wave scattering problems, both magnitudes and phases of the isolated resonances can be correctly obtained by using the proposed formalism while previous works based on the classical resonance scattering theory can give only magnitude correctly. The reason previous works could produce correct magnitude information for acoustic wave scattering (no mode conversion) is explained. Plane compressive wave scattering from a variety of submerged bodies is analyzed by utilizing the proposed resonance scattering function and then the isolated resonances are compared with previously published results. The exact radians phase shifts through the resonances and at the anti-resonances caused by the interaction between adjacent resonances, which has never been reported before, shows that the proposed formalism properly extracts the resonances from each partial waves. Due to the different ...