Resonant elastic scattering by a finite number of cylindrical cavities in an elastic matrix

Abstract The scattering of elastic waves by a finite number of close cylindrical cavities embedded in an elastic matrix is considered. Depending on whether the cavities are empty or fluid-filled, the regimes of interaction between the scatterers, resonant and interferential, are identified and compared with the ones already investigated in the case of elastic scatterers immersed in a fluid. To this end, the general formalism of the elastic scattering by N inclusions has been introduced. Numerical results are given for one, two and three identical inclusions. The related scattering S -matrix is next defined. Its unitarity allows indeed to express the energy conservation and consequently to check the numerical results. For empty cavities, the computations show that the interferential interaction is predominant even for very close cavities. In the case of fluid-filled cavities, a strong resonant coupling occurs with the emergence of a large number of resonances, while the interferential phenomenon appears only for large distances between scatterers. The resonant interaction examination shows new and unknown resonant interaction mechanisms. Indeed, except for a few narrow resonances, the single fluid-filled cavity resonances do not obey anymore the splitting law existing for immersed elastic scatterers: they split into a number of interaction resonances which is not in relation with the number of scatterers.