High-frequency diffraction by a shell

A stationary diffraction problem of acoustic wave by a thin elastic cylindrical shell is considered. The wave field (the potential of the speeds of the medium particles) has to satisfy the Helmholtz equation as well as the radiation conditions at infinity and the condition for equality of normal components of the speeds of the particles of the medium and the shell. The last one and the equations of the theory of the thin elastic shell (Kirhgoff-Ljav equations) allows us to derive the boundary condition for the wave field. It contains the tangential derivatives up to the sixth order. The problem of diffraction on a non-momentum circular shell is considered as a model. The solution of the model problem clarifies the type of asymptotic expansion (ansatz) for the wave field in the problem of diffraction by a convex shell of an arbitrary form. The wave field scattered in the bright region is represented by uniform asymptotic expansion in inverse powers of frequency. It contains 3 terms corresponding to the direct, reflected and head waves. The last one is closely connected with the lengthwise oscillations of the shell.