Vibrations of a gyroscopic meridian-plane sensor in a fluid suspension

Nikitina, N. V.; Tsidylo, I. V.

doi:10.1007/bf00847160

Int Appl Mech

1994

DOI: 10.1007/bf00847160

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Vibrations of a gyroscopic meridian-plane sensor in a fluid suspension

N. V. Nikitina¹,

I. V. Tsidylo²

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2005

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“…Averaging is admissible in both systems with hydrodynamic friction [5] and systems with dry friction. An averaged system makes it possible to establish the conditions for stable motion.…”

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confidence: 99%

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Nonlinear Oscillations in a System with Dry Friction

Martynyuk

Nikitina

2005

Int Appl Mech

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The case is examined where the right-hand side of the equations of motion is discontinuous. Attraction only in the stick domain ensures existence of periodic oscillations. Sufficient stability conditions for the periodic solution of a nonlinear system with dry friction are establishedIn this paper, we examine stable nonlinear oscillations that occur in a system with dry friction when the representative point falls into the domain where the right-hand side of the equations of motion is discontinuous. Averaging is admissible in both systems with hydrodynamic friction [5] and systems with dry friction. An averaged system makes it possible to establish the conditions for stable motion. The frictional force in a system with dry friction has a discontinuity. In one case, the representative point does not reach the discontinuity point during motion; then the attracting trajectory may produce self-oscillations and the average procedure is pertinent. In the other case, the closure of the phase trajectory is due to the attraction only in the neighborhood of the discontinuity point. This neighborhood is called the stick domain. By averaging, we can show that the solution is repelled on almost entire closed trajectory. This is an anbormal case of stable motion of a nonlinear system. The case is also known where the limit cycle of the Van der Pol equation with large parameter also has a repelling trajectory [6].The objective of the study is to demonstrate that the stable periodic oscillations of a nonlinear system can be due to sticking near the discontinuity point of the right-hand side of the equations of motion rather than due to the attraction of the phase trajectory. We will establish the quality of a stable closed trajectory using well-known results from the theory of oscillations [1].

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“…Averaging is admissible in both systems with hydrodynamic friction [5] and systems with dry friction. An averaged system makes it possible to establish the conditions for stable motion.…”

mentioning

confidence: 99%

“…Inequalities (10) and (11) hold for the parameter values (5). If condition (11) is satisfied, then the trajectory gives rise, at the point (x 1 1 = ,~* x x 2 2 = − =-0.14), to a stick domain in which it has an attracting solution.…”

mentioning

confidence: 99%

Nonlinear Oscillations in a System with Dry Friction

Martynyuk

Nikitina

2005

Int Appl Mech

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Vibrations of a gyroscopic meridian-plane sensor in a fluid suspension

Cited by 1 publication

References 1 publication

Nonlinear Oscillations in a System with Dry Friction

Nonlinear Oscillations in a System with Dry Friction

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