Complex vibrations of closed cylindrical shells of circular cross section and finite length subjected to nonuniform sign-changeable external load in the frame of classical nonlinear theory are studied. A transition from partial differential equations to ordinary differential equations (Cauchy problem) is carried out using the higher order Bubnov–Galerkin’s approach and Fourier’s representation. On the other hand, the Cauchy problem is solved using the fourth-order Runge–Kutta method. Results are analyzed owing to the application of nonlinear dynamics and qualitative theory of differential equations. The present work is devoted to the analysis of influence of the system dynamics of the following parameters: length of pressure width , relative linear shell dimension , and frequency and amplitude of external transversal load. Some new scenarios of vibrations of closed cylindrical shells exhibiting a transition from harmonic to chaotic vibrations are illustrated and studied.
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e-mail: awrejcew@p.lodz.pl
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January 2007
Research Papers
Routes to Chaos Exhibited by Closed Flexible Cylindrical Shells
J. Awrejcewicz,
J. Awrejcewicz
Department of Automatics and Biomechanics (K-16),
e-mail: awrejcew@p.lodz.pl
Technical University of Łódź
, 1/15 Stefanowskiego Street, 90-924 Łódź, Poland
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V. Krysko,
V. Krysko
Department of Higher Mathematics,
e-mail: tak@san.ru
Technical University of Saratov
, Politehnicheskaya Street, 77, 410054 Saratov, Russia
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N. Saveleva
N. Saveleva
Department of Higher Mathematics,
e-mail: qarx@mail.ru
Technical University of Saratov
, Politehnicheskaya Street, 77, 410054 Saratov, Russia
Search for other works by this author on:
J. Awrejcewicz
Department of Automatics and Biomechanics (K-16),
Technical University of Łódź
, 1/15 Stefanowskiego Street, 90-924 Łódź, Polande-mail: awrejcew@p.lodz.pl
V. Krysko
Department of Higher Mathematics,
Technical University of Saratov
, Politehnicheskaya Street, 77, 410054 Saratov, Russiae-mail: tak@san.ru
N. Saveleva
Department of Higher Mathematics,
Technical University of Saratov
, Politehnicheskaya Street, 77, 410054 Saratov, Russiae-mail: qarx@mail.ru
J. Comput. Nonlinear Dynam. Jan 2007, 2(1): 1-9 (9 pages)
Published Online: September 18, 2006
Article history
Received:
June 15, 2005
Revised:
September 18, 2006
Citation
Awrejcewicz, J., Krysko, V., and Saveleva, N. (September 18, 2006). "Routes to Chaos Exhibited by Closed Flexible Cylindrical Shells." ASME. J. Comput. Nonlinear Dynam. January 2007; 2(1): 1–9. https://doi.org/10.1115/1.2402923
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