Parametric vibrational resonance in a gyroscope driven by dual-frequency forces

Oyeleke, Kehinde S.; Olusola, O. I.; Vincent, U. E.; Ghosh, Dibakar; McClintock, Peter V. E.

doi:10.1016/j.physleta.2020.127040

Cited by 22 publications

(15 citation statements)

References 60 publications

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“…Figures 2-4 show the effects of passive control on the amplitudes of the oscillations. )ese figures are obtained by numerically solving equation (11) with fixed parameters [1][2][3], ω 0 � 4.89; μ � 8.5; λ � 1.7625;…”

Section: Harmonic Oscillations' States and Stabilitymentioning

confidence: 99%

“…It is therefore in the sense of understanding the influence of damping on the dynamics of gyroscopes that Chen modeled the dynamics of a gyroscope subjected to a cubic dissipation force [2]. )e study of the rotating gyroscope under the influence of the nonlinear damping force has made it possible to understand that the gyroscope under given conditions has a complex dynamic [1][2][3][9][10][11][12][13]. Of these behaviors, the most complex are chaotic movements and the phenomenon of multistability [1].…”

Section: Introductionmentioning

confidence: 99%

“…Of these behaviors, the most complex are chaotic movements and the phenomenon of multistability [1]. Several works have attempted to propose modes of control or synchronization of the chaotic gyroscopes according to the field of application of the gyroscope and its intended interest [2][3][4][5][6][11][12][13][14][15][16][17]. Multistability is one of the complex phenomena encountered in nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Dynamics of a Nonlinear Damping Gyroscope and Its Passive Control

Hounnan

Miwadinou

Monwanou

2023

Journal of Control Science and Engineering

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This article deals with the analysis of the effects of passive control on the complex dynamics of a nonlinear damping gyroscope. After modeling the gyroscope dynamics under the influence of the control force, using the harmonic balance method, the amplitudes of the harmonic oscillations are determined. Subsequently, the Routh–Hurwitz criterion is used to analyze and determine the stability domains of the oscillations. The influence of the control force parameters on the amplitude of the oscillations is studied. The control of chaotic dynamics and the coexistence of gyroscope attractors are performed through bifurcation diagrams, Lyapunov exponents, phase portraits, and time series. Numerical simulations are used to confirm the effectiveness of the control force. This article revealed that the amplitude of the harmonic oscillations, the chaotic dynamics, and the coexistence of the attractors of the rotating gyroscope are better controlled when the latter vibrates in the opposite direction to the passive control force.

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Section: Harmonic Oscillations' States and Stabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear Dynamics of a Nonlinear Damping Gyroscope and Its Passive Control

Hounnan

Miwadinou

Monwanou

2023

Journal of Control Science and Engineering

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“…Various types of resonance can be realized in nonlinear systems such as the stochastic resonance [1,2], coherence resonance [3,4], auto resonance [5,6], ghost resonance [7][8][9], chaos resonance [10,11], parametric resonance [12,13] and vibrational resonance [14][15][16][17][18]. The present paper is concerned with vibrational resonance.…”

Section: Introductionmentioning

confidence: 99%

“…This phenomenon was originally discovered by Landa and McClintok [14] in a bistable system. More recently, Oyeleke et al [12] studied the occurrence of VR in the gyroscope model driven by dual-frequency forces such as a parametric excitation and an additive periodic force. In addition to the well-known method of tuning the strength of the high-frequency field in VR, they have shown that the occurrence of VR in this model when the low-frequency parametric excitation is tuned.…”

Section: Introductionmentioning

confidence: 99%

Effect of Modulated Signals on Vibrational Resonance in a Harmonically Trapped Potential System

Bhuvaneshwari¹,

Priyatharsini²,

Chinnathambi³

et al. 2021

J. Sci. Res.

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We consider a harmonically trapped potential system driven by modulated signals with two widely different frequencies ω and Ω, where Ω >> ω. The forms of modulated signals are amplitude modulated (AM) and frequency-modulated (FM) signals. An amplitude-modulated external signal is consisting of a low-frequency (ω) component and two high-frequencies (Ω + ω) and (Ω − ω) whereas the frequency modulated signal consisting of the frequency components such as f sinωt cos(g cosΩt) and f sin(g cosΩt) cosωt. Depending upon the values of the parameters in the potential function, an odd number of potential wells of different depths can be generated. We numerically investigate the effect of these modulated signals on vibrational resonance (VR) in single-well, three-well, five-well and seven-well potentials. Different from traditional VR theory in the present paper, the enhancement of VR is made by the amplitudes of the AM and FM signals. We show the enhanced response amplitude (Q) at the low-frequency ω, showing the greater number of resonance peaks and non-decay response amplitude on the response amplitude curve due to the modulated signals in all the potential wells. Furthermore, the response amplitude of the system driven by the AM signal exhibits hysteresis and a jump phenomenon. Such behavior of Q is not observed in the system driven by the FM signal.

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