Resonance and vibration control of two-degree-of-freedom nonlinear electromechanical system with harmonic excitation

Amer, Y. A.

doi:10.1007/s11071-015-2121-2

Cited by 10 publications

(3 citation statements)

References 25 publications

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“…And there are some period windows in the chaotic motion process, which is one of the typical characteristics of chaotic motion of nonlinear systems. With the further increase of ω, chaotic motion will degenerate into periodic motion [20]. When c=2.65, as shown in Figures 3.1 and 3.2, the phase plan of the system is not repeated but chaotic.…”

Section: System Mechanics and Chaotic Motionmentioning

confidence: 96%

RBF Neural Network for Chaotic Motion Control of Collision Vibration System

Zhou

2024

SCPE

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Aiming at the control problem of chaotic motion of a kind of collision vibration system with gap, a chaotic motion control of collision vibration system based on RBF neural network is proposed. Firstly, the system mechanical model and chaotic motion are introduced, and then a chaotic controller based on RBFNN is designed to control and simulate the chaotic attractor. The model information of the system is not used in the control method. In this paper, the model of the system is used only to generate the input / output data of the system, and it is not used for the design of the controller. The parameters of AHGSA algorithm are set as follows: the population size is 30, the maximum number of iterations is 100,G0, a = 18, and the proportional coefficient P = 0.96. Small disturbances are applied to the controllable parameter ωof the system to suppress the chaotic motion of the system and make the system tend to stable periodic motion. In order to more clearly show the control effect of chaotic motion, the chaotic motion is controlled when the system iterates 400 times. The results show that the chaotic motion can be quickly controlled to periodic 1-1 motion, the phase diagram is a closed curve, and there is a peak in the spectrum diagram. Chaotic motion can be quickly controlled as periodic 2-2 motion, the phase diagram is two closed curves, and two obvious peaks appear in the spectrum diagram. The proposed method can effectively control the chaotic motion of the system, and the expected target can be not only the fixed point of period 1, but also other periodic orbits.

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Section: System Mechanics and Chaotic Motionmentioning

confidence: 96%

RBF Neural Network for Chaotic Motion Control of Collision Vibration System

Zhou

2024

SCPE

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“…Various methods for controlling chaos have been used in dynamical systems; the OGY method was presented by Ott et al [40] and had been applied in the dynamic game model to control chaos [41,42], a modified straight-line stabilization method [12], adaptive control [13], time-delayed feedback method [43], and other feedback control methods [6][7][8] had also been studied for the chaos control in an economic model with homogeneous or heterogeneous expectations. It can be known from previous works that feedback and parameter variation are two effective methods [9,12,13,16,27,28,[40][41][42][43][44], to achieve chaos control. Recently, a new control method called as control strategy of the state variables feedback and parameter variation was proposed [45] and had been used in the work of [8,13,26].…”

Section: Chaos Controlmentioning

confidence: 99%

A Dynamic Stackelberg–Cournot Duopoly Model with Heterogeneous Strategies through One-Way Spillovers

Jian-jun

Huang

2020

Discrete Dynamics in Nature and Society

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Many works studied on complex dynamics of Cournot or Stackelberg games, but few references discussed a dynamic game model combined with the Cournot game phase and Stackelberg game phase. Under the assumption that R&D spillovers only flow from the R&D leader to the R&D follower, a duopoly Stackelberg–Cournot game with heterogeneous expectations is considered in this paper. Two firms with different R&D capabilities determine their R&D investments sequentially in the Stackelberg R&D phase and make output decisions simultaneously in the Cournot production phase. R&D spillovers, R&D investments, and technological innovation efficiency are introduced in our model. We find that: (i) the boundary equilibrium of the dynamic Stackelberg–Cournot duopoly system, where two players adopt boundedly rational expectation and naïve expectation, respectively, is unstable if the Nash equilibrium of the system is strictly positive. (ii) The Nash equilibrium of the dynamic Stackelberg–Cournot duopoly system, where two players adopt boundedly rational expectation and naïve expectation, respectively, is locally asymptotically stable only if the model parameters meet certain conditions. Especially, results indicate that small value of R&D spillovers or big value of output adjustment speed may yield bifurcations or even chaos. Numerical simulations are performed to exhibit maximum Lyapunov exponents, bifurcation diagrams, strange attractors, and sensitive dependence on initial conditions to verify our findings. It is also shown that the chaotic behaviors can be controlled with the state variables feedback and parameter variation method.

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“…Siewe and Buckjohn [13] investigated the heteroclinic motion associated to a Melnikov-like investigation, energy transfer, and harvesting in coupled oscillator with nonlinear magnetic coupling. Amer [14] studied the behavior, stability, approximate solutions, active feedback control of a nonlinear electromechanical seismograph system with time-varying stiffness and he compared the numerical solution with perturbation one. Eissa et al [15] investigated the effects of saturation phenomena on nonlinear oscillating systems under multi-parametric or external excitation forces.…”

Section: Introductionmentioning

confidence: 99%

Active vibration suppression of a nonlinear electromechanical oscillator system with simultaneous resonance

Hamed¹,

Sayed²,

Alshehri³

2018

J. vibroeng.

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In this paper, we explored the nonlinear dynamics behavior and vibration suppression of a nonlinear electromechanical oscillator system under harmonic and parametric excitation. The model comprises of an electrical part coupled to mechanical part and displayed by a coupled nonlinear ordinary differential equations. The analytical up to second order approximate solutions are sought applying the method of multiple scales method. We utilized the time-series and method of averaging to analyze the response and stability of the solutions at the worst resonance cases. We checked the results of perturbation solution through numerical simulations and the effects of different system parameters have been reported. Comparison between analytical and numerical solutions is obtained. Also, the numerical results are obtained using MAPLE and MATLAB algorisms.

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Resonance and vibration control of two-degree-of-freedom nonlinear electromechanical system with harmonic excitation

Cited by 10 publications

References 25 publications

RBF Neural Network for Chaotic Motion Control of Collision Vibration System

RBF Neural Network for Chaotic Motion Control of Collision Vibration System

A Dynamic Stackelberg–Cournot Duopoly Model with Heterogeneous Strategies through One-Way Spillovers

Active vibration suppression of a nonlinear electromechanical oscillator system with simultaneous resonance

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