Axisymmetric Collision Problem for Two Identical Elastic Solids of Revolution

A direct central collision of two identical bodies of revolution is studied. A nonstationary mixed boundary-value problem with an unknown moving boundary is formulated. Its solution is represented by a series in term of Bessel functions. An infinite system of Volterra equations of the second kind for the unknown expansion coefficients is derived by satisfying the boundary conditions. The basic characteristics of the collision process are determined depending on the curvature of the frontal surface of the bodies     

Application of asymptotic methods to the investigation of one-frequency nonlinear oscillations of cylindrical shells interacting with moving fluid

We demonstrate the applicability of the Bogolyubov-Mitropol’skii asymptotic method to the construction of one-frequency solutions of a system of nonlinear equations used to describe the multimode free, forced, and parametrically excited vibrations of cylindrical shells interacting with moving fluid. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 4, pp. 476–487, April, 2007.