Abstract
Acoustic scattering by a pair of identical parallel cylinders is studied by emphasizing the role of the symmetries of the scatterer. Incident and scattered fields are expanded over the different irreducible representations ofC2v, the symmetry group of the scatterer. Then, from the boundary conditions, one obtains an infinite set of four linear complex algebraic equations (each one associated with a representation) where the unknown coefficients of the scattered fields are uncoupled. This method significantly simplifies the numerical treatment of the problem. As a consequence, positions of the scatterer resonances are determined in the complex plane of the reduced frequency and a partial algebraic classification of the resonances is obtained for various boundary conditions (soft cylinders, hard cylinders and elastic cylinders immersed in water). A physical interpretation of certain resonances in terms of trapped geometrical paths is provided.
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