Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback

El-Bassiouny, A F

doi:10.1155/2006/842318

Cited by 15 publications

(7 citation statements)

References 29 publications

(33 reference statements)

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“…Hence, it is necessary to further explore the stability including different physical parameters in the stable and the unstable solution regions. represented by the 'tongue' shape with the change in the detuning parameter [32], and the amplitude is stable when σ is small. These calculated results verify the early inference that smaller σ is of benefit to the steady-state vibration of the rotor system.…”

Section: Stability Analysismentioning

confidence: 99%

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

Zhou

Qiu

Zhang

et al. 2018

TFAMENA

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Steady-state vibration response characteristics of a motion model of a centrifugal pump rotor system with weak nonlinear stiffness have been calculated by using the multiple scale method (MSM). The theoretical results were in good agreement with the numerical results. Based on the MSM and the numerical method, the effects of detuning parameter, nonlinear stiffness parameter and natural frequency on steady-state amplitude were also investigated. Finally, Lyapunov's theorem on stability in the first approximation was applied for the determination of the system's stable and unstable solution regions. The calculated results imply that the centrifugal pump rotor system with weak nonlinear stiffness exhibits typical nonlinear vibration characteristics. The variation of detuning parameter, nonlinear stiffness parameter and natural frequency can result in a jump phenomenon, and their corresponding curves present 'hard spring', 'soft spring' and 'S'-shaped amplitude characteristic, respectively. Smaller detuning parameter and natural frequency or greater nonlinear stiffness parameter are beneficial to decreasing the steady-state response amplitude. The results can provide reference for an investigation into nonlinear vibration characteristics of a centrifugal pump rotor system.

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Section: Stability Analysismentioning

confidence: 99%

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

Zhou

Qiu

Zhang

et al. 2018

TFAMENA

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“…Substituting (20) into (12) and (13), using (15) and (16), and keeping only the linear terms in ρ 1 and φ 1 , one obtains…”

Section: Primary Resonancementioning

confidence: 99%

“…The stability of the steady-state subharmonic resonance is determined by substituting (20) into (34) and (35) and linearizing the resulting equations to obtain…”

Section: Subharmonic Resonance Of Order One-thirdmentioning

confidence: 99%

“…Li et al [19] studied the nonlinear dynamics of a Duffing-van der Pol oscillator under linear-plusnonlinear state feedback control with time delay. ElBassiouny [20] investigated fundamental and subharmonic resonances of harmonical oscillation with delay state feedback. Kouda and Mori [21] analyzed a ring of mutually coupled van der Pol oscillators with coupling delay.…”

Section: Introductionmentioning

confidence: 99%

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Vibration Control of a Cantilever Beam with Time Delay State Feedback

El-Bassiouny

2006

Zeitschrift Für Naturforschung A

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The primary and subharmonic resonance of order one-third of a cantilever beam under state feedback control with a time delay are investigated. Using the method of multiple scales, we obtain two slow flow equations for the amplitude and phase. The first-order approximate solution is derived and the effect of time delay on the resonance is investigated. The concept of an equivalent damping, related to the delay feedback, is proposed and an appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. The fixed points corresponding to the periodic motion of the starting system are determined, and the frequency-response and external excitation-response curves are shown. Bifurcation analysis is conducted in order to examine the stability of the system.

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“…Recently, the effect of feedback control with time delay on dynamics of such complex systems has become a new interest of investigators [12]. ELBassiouny [13] studied the fundamental resonance and subharmonic resonance of order one-half of a harmonically forced oscillation under state feedback control with a time delay by using the multiple scale perturbation technique. Li Jun et al [14] investigated the high-amplitude response suppression of the primary resonance of a nonlinear plant under cubic velocity feedback by means of the multiple scales method.…”

Section: Introductionmentioning

confidence: 99%

The Principal Parametric Resonance of Coupled van der Pol Oscillators under Feedback Control

Zhang

2012

Shock and Vibration

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Abstract. The principal parametric resonance of two van der Pol oscillators under coupled position and velocity feedback control with time delay is investigated analytically and numerically on the assumption that only one of the two oscillators is parametrically excited and the feedback control is linear. The slow-flow equations are obtained by the averaging method and simplified by truncating the first term of Taylor expansions for those terms with time delay. It is found that nontrivial solutions corresponding to periodic motions exist only for one oscillator if no feedback control is applied although the two oscillators are nonlinearly coupled. Based on Levenberg-Marquardt method, the effects of excitation and control parameters on the amplitude of periodic solutions of the system are graphically given. It can be seen that both of the two oscillators can be excited in periodic vibration with proper feedback. However, the amplitudes of the periodic vibrations are independent of the sign of feedback gains. In addition, the influence of time delay on the response of the system is periodic. In terms of numerical simulations, it is shown that both of the two oscillators can also have quasi-periodic motions, periodic motions about a new equilibrium position and other complex motions such as relaxation oscillation when feedback control is considered.

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Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback

Cited by 15 publications

References 29 publications

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

Vibration Control of a Cantilever Beam with Time Delay State Feedback

The Principal Parametric Resonance of Coupled van der Pol Oscillators under Feedback Control

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