Chaotic Interaction Dynamics of Three Structures: Two Cylindrical Shells Nested into Each Other and Their Reinforcing Local Rib
V. A. Krysko, S. S. Vetsel', V. V. Dobriyan, O. A. Saltykova
Gagarin Saratov State Technical University, Saratov, 410054 Russia
Keywords: хаотическая динамика, метод конечных элементов, замкнутая цилиндрическая оболочка, балка, контактное взаимодействие, хаотическая синхронизация, chaotic dynamics, finite element method, closed cylindrical shell, beam, contact interaction, chaotic synchronization
Abstract
This paper studies the chaotic dynamics of two cylindrical shells nested into each other with a gap and their reinforcing beam, also with a gap, which is subjected to a distributed alternating load. The problem is using methods of nonlinear dynamics and qualitative theory of differential equations. The basic equations are the Novozhilov equations for equations geometrically nonlinear structures. Contact pressure is determined by Kantor's method. Using finite elements in the spatial variables, the partial differential equations for the beam and shells are reduced to the Cauchy problem, which is solved by explicit integration (Euler's method). The chaotic synchronization of this system is studied.
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