On the equilibrium position stability of discrete model of filling hose under the action of reactive force

Baikov, A.E.; Mayorov, A. Y.

doi:10.20537/nd1501007

Cited by 2 publications

(1 citation statement)

References 4 publications

(10 reference statements)

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“…Certain sufficient conditions for the stability and instability of equilibrium were obtained in [8][9][10][11]. The destabilization areas of the rod nonconservative mechanical systems were investigated in [12][13][14]. Some investigations of oscillations and stability in nonconservative systems with an arbitrary number of degrees of freedom are presented in [15].…”

Section: Introductionmentioning

confidence: 99%

On Ziegler Effect with Arbitrary Large Viscous Friction

Krasil’nikov,

Maiorov

2022

Nelin. Dinam.

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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.

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Section: Introductionmentioning

confidence: 99%

On Ziegler Effect with Arbitrary Large Viscous Friction

Krasil’nikov,

Maiorov

2022

Nelin. Dinam.

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The features of solutions of dynamical systems with an external exciting load and non-conservative dynamical systems with pairwise interaction of degrees of freedom

Kashfutdinov

Georgiev²

2021

EJSI

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When mathematical models are developed, as a rule, a number of assumptions is done, which makes it possible to simplify the model, reduce its dimension and simulation time, or use the dimension reduction method. When modeling non-conservative systems with pairwise interaction of degrees of freedom, e.g. mechatronic systems, an elastic aircraft in a flow, an aeroelastic aircraft with an automated control system, etc., there is a desire to reduce the problem to a conservative dynamic system with harmonic action. The study shows that despite the apparent similarity of the tasks, they have significant differences that cannot be ignored. Differences in the behavior of conservative dynamical systems and non-conservative dynamical systems with pair interaction of degrees of freedom are considered. The results are demonstrated on the simplest example with an analytical solution, and in the finite element software package MSC.Nastran. The results of the solution in MSC.Nastran are compared with the results of the analytical solution.

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On the equilibrium position stability of discrete model of filling hose under the action of reactive force

Cited by 2 publications

References 4 publications

On Ziegler Effect with Arbitrary Large Viscous Friction

On Ziegler Effect with Arbitrary Large Viscous Friction

The features of solutions of dynamical systems with an external exciting load and non-conservative dynamical systems with pairwise interaction of degrees of freedom

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