Koval’chuk P. S.
Application of asymptotic methods to the investigation of one-frequency nonlinear oscillations of cylindrical shells interacting with moving fluid
Ukr. Mat. Zh. - 2007. - 59, № 4. - pp. 476–487
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.
Application of the Averaging Method to the Investigation of Nonlinear Wave Processes in Elastic Systems with Circular Symmetry
Ukr. Mat. Zh. - 2001. - 53, № 10. - pp. 1358-1367
We apply asymptotic methods of nonlinear mechanics (the Bogolyubov–Mitropol'skii averaging method) to the construction of approximate solutions of a system of nonlinear equations describing wave processes in elastic systems with circular symmetry. As an example, we study the dynamics of interaction of two flexural waves that propagate in a cylindrical shell under the conditions of free oscillations and periodic excitation.