 | | 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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| L. P. Dzubak, G. V. Manucharyan, Yu. V. Mikhlin, and T. V. Shmatko, "Stability of regular and chaotic vibration modes in systems with several equilibrium states," Mech. Solids. 41 (2), 134-143 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
2 |
Pages |
134-143 |
| Title |
Stability of regular and chaotic vibration modes in systems with several equilibrium states |
| Author(s) |
L. P. Dzubak (Kharkov)
G. V. Manucharyan (Kharkov)
Yu. V. Mikhlin (Kharkov)
T. V. Shmatko (Kharkov) |
| Abstract |
Forced vibrations of a system with two degrees of freedom and several
equilibrium states are considered. Such systems can be obtained by discretizing
elastic systems in a post-critical state. The modes of vibrations that are
periodic if the amplitude of the external periodic excitation is small and
become chaotic as this amplitude increases are studied. To investigate the
stability of such vibration modes, computational procedures based on the
classical definition of the Lyapunov stability are utilized. The stability of
vibration modes of nonlinear rods, shells, and arches is analyzed.
The mutual instability of the phase trajectories is utilized as a criterion of
the appearance of the chaotic behavior in a nonlinear system. Trajectories with
very close initial conditions are compared. The computational procedures based
on the classical definitions of the Lyapunov stability enable one to judge the
stability or instability of these trajectories. Specific calculations for the
time-varying Duffing equation and the von Mises truss allow one to observe the
appearance and expansion of the chaotic behavior domains. |
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|
| Received |
20 August 2002 |
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