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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
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
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
Linking options:
https://www.mathnet.ru/eng/nd784 https://www.mathnet.ru/eng/nd/v18/i2/p161
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Abstract page: | 86 | Full-text PDF : | 28 | References: | 18 |
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