surface waves, edge waves, Rayleigh wave, elastic hollow cylinder, elastic shell, asymptotic methods.

 Lower order waves propagating along the edge of a semi-infinite circular cylindrical shell are studied. The 3D equations of elasticity in cylindrical coordinates are used for describing of vibrations of the shell. The solution of 3D problem is presented as modal expansion with non-axisymmetric modes of a hollow cylinder. In the long-wave domain, the results of numerical investigation confirm the existence of two fundamental edge waves established before only in the framework of Kirchhoff–Love theory of shells. They are the ” antisymmetric“ wave corresponding to flexural edge wave in the theory of shells and the ” symmetric“ wave corresponding to tangential edge wave. The short-wave limits of the velocities of these wave are the velocities of the waves localized near the ridge of a quarter-space and propagating on the outer and the inner circumference of the front edge, respectively. The graph for the imaginary part of the frequency which characterizes the damping of the ” symmetric“ wave caused by the propagating modes is presented.

1. Ardazishvili Roman Vyacheslavovich e-mail: ardazishvili.roman@yandex.ru, Postgraduate student, Department of Mathematical Theory of Elasticity and Biomechanics, Saratov State University, Saratov, Russia. 2. Wilde Maria Vladimirovna e-mail: mv_wilde@mail.ru, Doctor of Science, Professor of Department of Mathematical Theory of Elasticity and Biomechanics, Saratov State University, Saratov, Russia. 3. Kossovich Leonid Yurjevich e-mail: president@sgu.ru, Doctor of Science, Head of Department of Mathematical Theory of Elasticity and Biomechanics, President of Saratov State University, Saratov State University, Saratov, Russia.