 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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| V. A. Krys'ko and T. V. Shchekaturova, "Chaotic vibrations of cone shells," Mech. Solids. 39 (5), 124-133 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
5 |
Pages |
124-133 |
| Title |
Chaotic vibrations of cone shells |
| Author(s) |
V. A. Krys'ko (Saratov)
T. V. Shchekaturova (Saratov) |
| Abstract |
Chaotic vibrations of deterministic, geometrically nonlinear, shallow, isotropic cone shells of revolution subjected to a cyclic load are studied. The influence of the inertial forces along the directions tangent to the middle surface and the rotational inertia of the normal cross-section are ignored. The Ritz method is utilized. The initial value problem for ordinary differential equations is solved by the Runge-Kutta fourth-order method.
The numerical analysis is based on the nonlinear dynamics and qualitative theory of differential equations. New scenarios for the transition of vibrations of flexible cone shells from harmonic to chaotic ones are discovered. The development of various types of vibration is studied as depending on a number of parameters, including the rise of the shell, the amplitude and frequency of the excitation force, and the number of terms preserved in series expansions of the basic functions. This enables one to consider an important issue of the approximation of a distributed system by a discrete one and to obtain an answer to the question whether the chaos disappears for sufficiently large number of terms preserved in the series expansions of the basic functions. |
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|
| Received |
22 May 2003 |
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