STOCHASTIC STABILITY OF NONLINEAR FLUCTUATIONS IN VISCOELASTIC BODIES
Abstract
The paper considers a wave dynamics of a viscoelastic body (Kelvin – Voight model) which is described by a system of nonlinear differential equations in partial derivatives. Transition from a system of partial derivatives to an ordinary differential equations system for the coordinate functions is executed with the purpose to study the system behavior over time using the Bubnov – Galerkin method.
A solution for one-dimensional case is obtained, which for negligible viscosity is reduced to the Duffing equation describing behavior of a nonlinear elastic rod in time at external actions. The paper shows that if an external influence is a deterministic periodic pulse process then oscillations starting from some time under certain conditions are transited into regime of deterministic chaos. In this case the stability can be investigated by criteria of probabilistic character. The paper considers stability of a nonlinear dynamical system in chaotic regime based on the mean-square criteria.
About the Authors
A. V. Chigarev
Belarusian National Technical University
Belarus
Belarus
Yu. V. Chigarev
Belarusian State Agrarian Technical University
Belarus
Belarus
S. A. Pronkevich
Belarusian National Technical University
Belarus
Belarus
References
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Review
For citations:
Chigarev A.V., Chigarev Yu.V., Pronkevich S.A. STOCHASTIC STABILITY OF NONLINEAR FLUCTUATIONS IN VISCOELASTIC BODIES. Science & Technique. 2012;(3):51-55. (In Russ.)
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