Nonlinear saturation controller for vibration supersession of a nonlinear composite beam

Hamed, Y. S.; Amer, Y. A.

doi:10.1007/s12206-014-0706-1

Cited by 24 publications

(19 citation statements)

References 32 publications

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“…The modified nonlinear differential equations describe the oscillations of the nonlinear composite beam model [23,24,26] are given by:…”

Section: Equations Of Motionmentioning

confidence: 99%

“…El-Ganaini et al [25] considered the PPF controller to put down the vibration amplitude of a nonlinear dynamic model at primary resonance with 1 : 1 internal resonance. Hamed and Amer [26] studied an active controller for damping out the nonlinear vibration composite beam with parametric excitation force in the case of 1 : 2 internal resonances. Sayed and Kamel [27] examined the effect of a linear controller to control the vibration of each of the saturation control of a linear absorber and the vibrating system.…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation analysis of a composite cantilever beam via 1:3 internal resonance

et al. 2020

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In this paper, we study a multiple scales perturbation and numerical solution for vibrations analysis and control of a system which simulates the vibrations of a nonlinear composite beam model. System of second order differential equations with nonlinearity due to quadratic and cubic terms, excited by parametric and external excitations, are presented. The controller is implemented to control one frequency at primary and parametric resonance where damage in the mechanical system is probable. Active control is applied to the system. The multiple scales perturbation (MSP) method is implemented to obtain an approximate analytical solution. The stability analysis of the system is obtained by frequency response (FR). Bifurcation analysis is conducted using various control parameters such as natural frequency (ω1), detuning parameter (σ1), feedback signal gain (β), control signal gain (γ), and other parameters. The dynamic behavior of the system is predicted within various ranges of bifurcation parameters. All of the stable steady state (point attractor), stable periodic attractors, unstable steady state, and unstable periodic attractors are determined efficiently using bifurcation analysis. The controller’s influence on system behavior is examined numerically. To validate our results, the approximate analytical solution using the MSP method is compared with the numerical solution using the Runge-Kutta (RK) method of order four.

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“…The modified nonlinear differential equations describe the oscillations of the nonlinear composite beam model [23,24,26] are given by:…”

Section: Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis of a composite cantilever beam via 1:3 internal resonance

et al. 2020

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“…7 indicates a comparison between the time histories and approximate modulated amplitudes of the electromechanical system after control approached by Eqs. (2a), (2b) and (29)- (32) respectively. In addition, Figs.…”

Section: Comparison Studymentioning

confidence: 99%

“…Also, they studied three cases of primary and internal resonance (1:2, 1:1, 1:1:3) and they compared the analytical results with the numerical one of the modal equations. Hamed and Amer [32] used different types of control algorithms and studied its effectiveness to reduce the large vibrations of a flexible composite beam system. Hamed et al [33] studied the stability and nonlinear oscillations of the MEMS gyroscope system under different types of parametric excitations.…”

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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“…Saturation active control method was initially proposed and studied in [24][25][26][27]. Other example of these systems that saturation phenomenon was applied are the L-shaped beam structure by [28,29] and the nonlinear saturation controller was applied for nonlinear beam by [30,31]. The nonlinear energy harvesting material in non-ideal problems with saturation phenomenon was introduced as in [3,[32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

On vibration mitigation and energy harvesting of a non-ideal system with autoparametric vibration absorber system

et al. 2018

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This paper demonstrates that vibration mitigation and energy harvesting can be achieved simultaneously by using of an electricity-generating from autoparametric vibration absorber system (AVAS) and non-ideal system (NIS). The NIS consists of a simple portal frame excited by a small dc motor with eccentric mass, with limited power supply and located on the top. The AVAS consists of a cantilever beam with tip mass parallel coupled to NIS. A piezoelectric material is considered for energy harvesting installed in the base of the AVAS and an electric circuit is connected to the piezoelectric material in order to produce voltage output. Several numerical simulations were carried out focusing on the passage through the resonance of NIS, when the motor rotational frequency is near the portal frame natural frequency and when the non-ideal subsystem frequency is approximately twice the absorber beam frequency (two-to-one internal resonance). The results showed the existence of Sommerfeld effect in NIS and saturation phenomenon in the NIS-AVAS.

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Nonlinear saturation controller for vibration supersession of a nonlinear composite beam

Cited by 24 publications

References 32 publications

Bifurcation analysis of a composite cantilever beam via 1:3 internal resonance

Bifurcation analysis of a composite cantilever beam via 1:3 internal resonance

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

On vibration mitigation and energy harvesting of a non-ideal system with autoparametric vibration absorber system

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