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Russian Journal of Nonlinear Dynamics, 2022, Volume 18, Number 2, Pages 161–170
DOI: https://doi.org/10.20537/nd220201
(Mi nd784)
 

Nonlinear physics and mechanics

On Ziegler Effect with Arbitrary Large Viscous Friction

P. S. Krasil'nikov, A. Yu. Maiorov

Moscow Aviation Institute (National research university), Volokolamskoe shosse 4, 125993, Moscow, Russia
References:
Abstract: We study a mechanical system with two degrees of freedom simulating the motion of rotor blades on an elastic bushing of a medium-sized helicopter. For small values of some problem parameters, the destabilizing effect due to small linear viscous friction forces has been studied earlier. Here we study the problem with arbitrary large friction forces for arbitrary values of the problem parameters. In the plane of parameters, the regions of asymptotic stability and instability are calculated. As a result, necessary and sufficient conditions for the existence of a destabilizing effect under the action of potential, follower forces and arbitrary friction forces have been obtained. It is shown that, if some critical friction coefficient $k_*$ tends to infinity, then there exists a Ziegler area with arbitrarily large dissipative forces.
Keywords: Non-conservative mechanical system, large linear dissipative forces, follower force, Ziegler's effect, Lyapunov's stability.
Received: 06.05.2021
Accepted: 24.04.2022
Bibliographic databases:
Document Type: Article
MSC: 70E50
Language: english
Citation: P. S. Krasil'nikov, A. Yu. Maiorov, “On Ziegler Effect with Arbitrary Large Viscous Friction”, Rus. J. Nonlin. Dyn., 18:2 (2022), 161–170
Citation in format AMSBIB
\Bibitem{KraMai22}
\by P. S. Krasil'nikov, A. Yu. Maiorov
\paper On Ziegler Effect with Arbitrary Large Viscous Friction
\jour Rus. J. Nonlin. Dyn.
\yr 2022
\vol 18
\issue 2
\pages 161--170
\mathnet{http://mi.mathnet.ru/nd784}
\crossref{https://doi.org/10.20537/nd220201}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4445313}
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