GENERALIZED DEBYE SERIES EXPANSION - PART-I - TREATMENT OF THE CONCENTRIC CYLINDRICAL FLUID-SOLID INTERFACES

In this paper, a new matrix formulation for the calculation of the sca ttered field due to a plane wave normally incident on a structure invo lving one or several concentric cylindrical fluid - elastic solid inte rfaces is presented. In this method, the generalized Debye series expa nsion (GDSE) is used to calculate the scattered field. The GDSE gives a decomposition of the global scattering process in a series of local interactions involving modal reflection and refraction (transmission) coefficients which are defined at each interface of the scatterer. A d etailed analysis of the scattering by elastic cylinders is presented i n order to introduce the modal reflection and refraction coefficients and to explain the GDSE construction. Local forms of energy conservati on laws and characteristic equations are expressed by means of the mod al reflection and refraction coefficients. The case of the elastic she ll immersed in a fluid is also treated and then the method is extended for the case of more complicated structures involving several fluid - elastic solid concentric interfaces. New modal reflection and refract ion coefficients related to shells and multilayers are defined. These new coefficients which simplify the structure of the GDSE also verify energy conservation laws.