Relanon between singularity expansion method(SEM) and resonance scattering theory(RST)

In recent years there are two theories for the acoustic scattering, one is the Singularity Expansion Method (SEM) , the other is the Resonance Scattering Theory (RST). In this paper, relation between these two theories was established. For the examples of the acoustic scattering from the solid elastic cylinder and sphere immersed in water, we prove that the RST can be directly derived from the SEM, so that these two theories are equivalent. By use of the Mittag- Leffler theorem we expand the pure elastic scattering wave, which is extracted by isolating the rigid background from the total scattering wave, in an exact resonance expansion. We specially prove that the reradiation efficiency and the resonance width are nearly proportional to the imaginary part of the corresponding pole for most solid objects immersed in water. This shows that the resonance scattering behavious can be entirely determined by the complex frequency poles. For the cases of an aluminum cylinder and a tungsten carbide sphere immersed in water, we calculate the partial-wave form functions by using the new resonance formulae. The results agree with the exact calculation well.

Pure elastic resonance scattering for submerged elastic objects with separable geometries

Theoretically, the extraction of resonance scattering spectra is performed by a pure elastic scattering function, which is defined as the total scattering function subtracts an appropriate background term. In this paper, we derive a simple and explicit expression of the pure elastic scattering function for the separable geometries immersed in water. It depends on the modal mechanical impedance and acoustic impedance except a phase factor only relative to the geometry Analyses used the new expression leads to two Kinds of resonances with distinguishable character: the elastic-borne wave resonances and the fluid-borne wave resonances. The former depends mainly on elasticity of the object and the fiuid-loading has secondary effect. The later is related closely with the liquid-loading and vanishes if the liquidloading vanishes. This allows us to classify the family of individual resonance correctly. Taking into account the contributions of the fluid-borne wave resonances, we modify the conventional resonance scattering formula by use of the Singularity Expansion Method.