Asymptotic Eigenmodes Localized Near the Edge of a Vessel, with Acoustic Medium, Which Is Covered by a Thin Elastic Membrane

The paper deals with the formal short-wavelength asymptotic solutions describing the acoustic eigenoscillations in a vessel having a hard bottom, filled in by an acoustic medium, and covered by a thin elastic membrane. The solutions are localized in the medium near the line of the rigid contact of the membrane covering the vessel with the edge of the vessel. The coefficients in the asymptotic expansion of the solutions satisfy a recurrent sequence of solvable problems, whereas the frequencies, for which such nontrivial formal solutions exist, obey an asymptotic ‘quantization-type condition.

DOI 10.1134/S1061920824030105