Regular and Chaotic Dynamics of Flexible Plates

Author:

Awrejcewicz J.12,Krylova E. Yu.3,Papkova I.V.3,Krysko V. A.3

Affiliation:

1. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski Street, 90-924 Lodz, Poland

2. Department of Vehicles, Warsaw University of Technology, 84 Narbutta Street, 02-524 Warszawa, Poland

3. Department of Mathematics and Modeling, Saratov State Technical University, Russian Federation, Politehnicheskaya 77, Saratov 410054, Russia

Abstract

Nonlinear dynamics of flexible rectangular plates subjected to the action of longitudinal and time periodic load distributed on the plate perimeter is investigated. Applying both the classical Fourier and wavelet analysis we illustrate three different Feigenbaum type scenarios of transition from a regular to chaotic dynamics. We show that the system vibrations change with respect not only to the change of control parameters, but also to all fixed parameters (system dynamics changes when the independent variable, time, increases). In addition, we show that chaotic dynamics may appear also after the second Hopf bifurcation. Curves of equal deflections (isoclines) lose their previous symmetry while transiting into chaotic vibrations.

Funder

National Center of Science

Publisher

Hindawi Limited

Subject

Mechanical Engineering,Mechanics of Materials,Geotechnical Engineering and Engineering Geology,Condensed Matter Physics,Civil and Structural Engineering

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