The scattering matrix in a waveguide with elastic walls (Q1820033)

The spectrum of normal waves is studied and the scattering matrix is determined for a planar waveguide with elastic walls and with an elastic semi-infinite plate situated within it. The mechanical mode of behaviour of elastic plates is described using the general-type differential operators. Problems of this type belong to the class of the boundary contact problems. The unique solvability of these problems requires the formulation of additional boundary contact conditions describing the mechanical behaviour of the edge of the semi-infinite plate situated within the waveguide. The regularization of the integrals appearing when the general-type boundary contact conditions are satisfied is indicated.