About the authors
| First name, Middle name, Last name, Scientific degree, Scientific rank, Current position. Full and brief name of the organization, The organization address. | Zagniboroda N.A. – post-graduate student E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Krysko V.A. – doctor of tecnical sciences, professor E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Krysko A.V. – doctor of physical and mathematical sciences, professor E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Saratov State Technical University The organization address: 413100, Russia, Engels, pl. Svoodi, 17 Shakirzyanov F.R. – candidate of physical and mathematical sciences, assistant E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it Kazan State University of Architecture and Engineering The organization address: 420043, Russia, Kazan, Zelenaya, 1 |
| Title of the article | Nonlinear dynamics of an infinitely long cylindrical panels |
| Abstract. | Flexible shallow infinitely long cylindrical panels are widely used in various electronic devices and gyroscopes – a micro-electro-mechanical systems (MEMS sensors) that are part of the model gyros with distributed mass and large amplitude oscillations of the oscillators. A mathematical model for the analysis of chaotic dynamics of infinitely long flexible cylindrical panels when, the model of the Kirchhoff-Love is used as a kinematic model, was built in this paper. Geometric nonlinearity is taken into account in the form of T. von Karman. Nonlinear partial differential equations are reduced to the Cauchy problem using the finite difference method with an error O(h2) and the finite element method. Cauchy problem is solved by Runge-Kutta method of the fourth and the sixth order of accuracy. The resulting maps oscillation modes for infinitely long flexible shallow cylindrical panels allow determining the permissible values of the control parameters. Substantiates the reliability of the results. |
| Keywords. | Bifurcation, phase portraits, Lyapunov exponents, chaotic vibrations of infinitely long cylindrical panels. |
| For citations: | Zagniboroda N.A., Krysko V.A., Krysko A.V., Shakirzyanov F.R. Nonlinear dynamics of an infinitely long cylindrical panels // Izvestiya KGASU. 2013. №3(25) P.144-153. |
