Back reflection of sound beam from an elastic cylinder at oblique incidence

The scattering of a bounded beam of ultrasound obliquely incident upon an elastic circular cylinder of infinite length is investigated. A cross-section of the wave beam is narrow in the axial direction of the cylinder and unbounded in the perpendicular direction, i.e. the sound beam is considered as an “acoustical knife”. This problem is solved by means of the exponential Fourier transform for the axial variable and the modal series for the polar variables. On basis of the high-frequency expansions and the steepest descent method (when the saddle point is located near the pole) the conditions of Rayleigh surface wave back reradiation are obtained