Application of zero-range models to the problem of diffraction by a small hole in elastic plate

Abstract

The theory of zero-range potentials is applied to the boundary-contact acoustics problem of diffraction by small round holes in elastic plates. First the set of all point models of small inhomogeneities, represented by zero-range potentials in L2 is constructed. Then the problem of choosing the model corresponding to the examined diffraction problem is simplified by decomposition of the model into two components. One corresponds to the case of an absolutely rigid plate, the other to the case of an isolated plate. Problems of diffraction for both components can be solved exactly by variables separation method. Comparing the far field asymptotics for these problems with that produced by point models one can find the parameters of the zero-range potential. When the potential is fixed the solution, being a number of leading terms in the asymptotical on the small radius of the hole decomposition of far field, is explicitly calculated.