Control of primary and subharmonic resonances of a Duffing oscillator via non-linear energy sink

Zulli, Daniele; Luongo, Angelo

doi:10.1016/j.ijnonlinmec.2015.08.014

Cited by 22 publications

(12 citation statements)

References 33 publications

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“…Indicating as the dimensionless displacement of the principle oscillator. The dimensionless equation of motion as presented in [8] is modified as:…”

Section: Mathematical Model and Controller Designmentioning

confidence: 99%

“…In a previous work [8], the authors studied the influence of the use of the NES for passive control vibration under bi-frequency harmonic force through considering and the (non-dimensional) displacement of the principle non-linear oscillator. They applied MSHBT, to find the relevant amplitude modulation equations.…”

Section: Comparison Between the Previous Work And This Workmentioning

confidence: 99%

“…Firstly, we adjusted the equation of Ref. [8] by considering only (non-dimensional) displacement of the principle non-linear oscillator. We utilized NIPPF absorber was offered as the best controller compared to the other controllers to control the vibration system as shown in this paper.…”

Section: Comparison Between the Previous Work And This Workmentioning

confidence: 99%

“…Using the method of multiple scales, an overall control pattern was analyzed. On the other hand, Zulli and Luongo [8] analyzed the impact of using the non-linear energy sink (NES) as a passive control for vibration relating primary and subharmonic resonance. There are three different situations had been taken into consideration, the first one is the external harmonic excitation: 1:1 resonance than, 1:3 resonance and finally concurrent 1:1 and1:3 resonance.…”

Section: Introductionmentioning

confidence: 99%

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The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

Amer¹,

EL-Sayed²,

Abdelwahab³

et al. 2019

J. vibroeng.

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In this paper, we applied three different control methods; Positive Position Feedback (PPF), Integral Resonance Control (IRC) and Nonlinear Integrated Positive Position Feedback (NIPPF) added to a Duffing oscillator system subjected to harmonic force. An analytic solution is introduced using the multiple scales perturbation technique (MSPT) to solve the nonlinear differential equations, which simulate the system with NIPPF controller. Before and after control at the primary and superharmonic resonances, the nonlinear systems' steady-state amplitude and stability are studied and examined. The influences of various parameters of the system after being connected to NIPPF are illustrated. Optimum working conditions for the NIPPF controller are obtained at internal resonance ratio 1:1. A Comparison is also made to validate the closeness between the numerical solution and the analytical perturbative one at time-history and frequency response curves (FRC). Finally, a comparison with the available results in the literature is presented. From this comparison, we find that the best control to the system is via the NIPPF controller.

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“…Indicating as the dimensionless displacement of the principle oscillator. The dimensionless equation of motion as presented in [8] is modified as:…”

Section: Mathematical Model and Controller Designmentioning

confidence: 99%

Section: Comparison Between the Previous Work And This Workmentioning

confidence: 99%

Section: Comparison Between the Previous Work And This Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

Amer¹,

EL-Sayed²,

Abdelwahab³

et al. 2019

J. vibroeng.

View full text Add to dashboard Cite

show abstract

“…Based on this mechanism, the NES has been widely designed to suppress the undesirable vibrations. [17][18][19] NES attached to continuum primary linear structures, such as rod, 20 beams, [21][22][23] drill-string, 24 plate, 25 elastic strings, 26 and hollow rotor systems 27 is considered in literatures. According to the NES applications, the NES has been designed to various types, like nonsmooth 28 or nonpolynomial.…”

Section: Introductionmentioning

confidence: 99%

Vibration power flow characteristics of the whole-spacecraft with a nonlinear energy sink

Zhang

Zhou

Wang

et al. 2019

Journal of Low Frequency Noise, Vibration and Active Control

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The power flow analysis approach is applied for quantitatively evaluating the dynamic performance of a nonlinear energy sink in the frequency domain. A two-degree-of-freedom model of the whole-spacecraft coupled to a nonlinear energy sink is considered. Analytical approximations and numerical integrations are performed for the integrated system. The time-averaged input and dissipated and absorbed powers of the system are formulated. Power absorption ratio is proposed as the vibration reduction performance indicator of the nonlinear energy sink and is compared with kinetic energy of the oscillator. Results show that the power absorption ratio of nonlinear energy sink is high at all frequencies except at an antiresonance region. The effects of varying nonlinear energy sink parameters on its vibration absorption performance are discussed. As observed, the nonlinear energy sink performs well with the increase in viscous damping of nonlinear energy sink in the high-frequency range. However, the nonlinear energy sink performs poorly in the lowfrequency range in the same case. Therefore, power flow analysis can provide great insight for nonlinear energy sink design in frequency domain and is suitable for practical engineering application.

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Influences of Temperature on Dynamic Behaviors of Suspended Cables Under Primary and Sub-Harmonic Excitations Simultaneously

Zhao

Lin

Chen

et al. 2020

Nonlinear Dynamics of Structures, Systems and Devices

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Control of primary and subharmonic resonances of a Duffing oscillator via non-linear energy sink

Cited by 22 publications

References 33 publications

The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

Vibration power flow characteristics of the whole-spacecraft with a nonlinear energy sink

Influences of Temperature on Dynamic Behaviors of Suspended Cables Under Primary and Sub-Harmonic Excitations Simultaneously

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