0
2013
Impact Factor

    Andrey Maiorov

    Publications:

    Krasil'nikov P. S., Maiorov A. Y.
    On Ziegler Effect with Arbitrary Large Viscous Friction
    2022, Vol. 18, no. 2, pp.  161-170
    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
    Citation: Krasil'nikov P. S., Maiorov A. Y.,  On Ziegler Effect with Arbitrary Large Viscous Friction, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 2, pp.  161-170
    DOI:10.20537/nd220201
    Baikov A., Maiorov A. Y.
    Abstract
    The destabilization of the stable equilibrium position of a non-conservative system with three degrees of freedom under the action of a linear viscous friction force is considered. The dissipation is assumed to be completed. The standard methods of the stability theory are using for solving problem. Stability of equilibrium position is studied in the linear approximation. The coefficients of characteristic polynomial are constructed by using Le Verrier’s algorithm. Ziegler’s effect condition and criterion for the stability are constructed by using perturbation theory. Stability of the three-link rod system’s equilibrium position is investigated, when there is no dissipative force. Ziegler’s area and criterion for the stability of the equilibrium position of a system with three degrees of freedom, in which the friction forces take small values, are constructed. The influence of large friction forces is investigated. The results of the study may be used for the analysis of stability of a non-conservative system with three degrees of freedom. Also, the threelink rod system may be used as discrete model of filling hose under the action of reactive force.
    Keywords: fillling hose, discrete model, three-link rod system, tracking force, dissipative forces, asymptotically stability, Ziegler’s effect, Ziegler’s areas, criterion for the stability
    Citation: Baikov A., Maiorov A. Y.,  On the equilibrium position stability of discrete model of filling hose under the action of reactive force, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 1, pp.  127-146
    DOI:10.20537/nd1501007

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