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About scenarios of transition plate oscillationsin chaotic by using the fourier’s analysis

Keywords:

E.Y. Krylova, V.A. Krysko, I.V. Papkova


The article is devoted to researching nonlinear oscillations of flexible, rectangular in plan plate under influence of shearing alternating load. The plate is the major element of various modern engineering constructions. Every day the character of outside dynamic pressure on elements of similar constructions is changing and its intensity is increasing. It results in essential complication of oscillations character. That is why it is necessary to research these oscillations on basis of qualitative theory of differential equations and nonlinear dynamics. In known literature publications of investigations nonlinear oscillations of flexible, rectangular in plan plate under influence of shearing alternating load are absent. The plate regards as continual system that is a system with infinite number of degrees of freedom. Initial differential equations of the flexible plates theory by Kirchhoff’s kinematic model was received by using the variational principles. The boundary conditions of resting on inextensible ribs and zero initial conditions are connected to differential equations. Infinite problem is reduced to finite dimensional problem using the finite difference method with approximation . Initial problem are solved by using the Runge – Kutt’s method for 4 order of accuracy. Time step is chosen by using Runge’s rule. Qualitative theory of ordinary differential equations is used to research nonlinear oscillations. Analysis of signal, phase-plane portraits, Poincare cross-sections, autocorrelation functions, and Fourier’s analysis are used too. Scenarios of transition oscillations of flexible, rectangular in plan plate under influence of shearing alternating load in chaotic by using the Fourier’s analysis are researched. As a result Ruelle -Takens-Newhouse’s scenarios for two different modifications and Feigenbaum’s scenario were received. The map of plate oscillations character under influence of outside shearing alternating load is constructed. It gives a chance to control of the system and avoid the dangerous routines of its work.
References:
June 24, 2020
May 29, 2020

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