Nonlinear vibration and of the Duffing oscillator to parametric excitation with time delay feedback

Amer, Y. A.; Elsayed, Ahmed; Kotb, A. A.

doi:10.1007/s11071-016-2840-z

Cited by 34 publications

(18 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Amer et al [13], studied the nonlinear oscillations with time delay feedback of a parametric excited Duffing oscillator system. The MSPT has been employed to find the frequency response equations (FRE).…”

Section: Introductionmentioning

confidence: 99%

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.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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.

Self Cite

View full text Add to dashboard Cite

show abstract

“…More recently, because of the importance of parametric excitation on electromechanical systems and devices, the e®ect of parametric excitation on energyharvesting systems has been investigated. [45][46][47] In these researches, a Du±ng oscillator has been used to model the behavior of energy harvesters. Besides, to study nonlinear vibration and stability of tapered-composite plate, a parametric excitation was employed.…”

Section: Introductionmentioning

confidence: 99%

Parametric Excitation of Pre-Stressed Graphene Sheets under Magnetic Field: Nonlinear Vibration and Dynamic Instability

Ghadiri

Hosseini

2019

Int. J. Str. Stab. Dyn.

View full text Add to dashboard Cite

Motivated by the lack of su±cient accuracy in investigation of nonlinear dynamics of graphene sheets (GS), nonlinear dynamic instability and frequency response of the pre-stressed single layered GS (SLGS) are investigated in the present paper. To achieve this aim, in the¯rst step, SLGS embedded on a visco-Pasternak foundation is modeled while it is under an initial stress and subjected to a parametric axial force and magnetic¯eld. Then, based on Eringen's theory, nonlinear von Karman relations and Kelvin-Voigt model, the nonlinear governing equation of motion is derived. In the next step, Galerkin technique and multiple time scales method are employed to analyze and solve the equation of motion. Emphasizing the e®ect of parametric excitation, for considering the instability regions, bifurcation points are discussed. As a result, a parametric study is conducted to show the importance of damping coe±cient and parametric excitation in dynamic instability of the system. Numerical examples are also treated which show various discontinuous bifurcations. Also, in¯nitely stable and unstable solutions are addressed.

show abstract

“…In recent years, a new trend of using chaotic oscillators as a solution has emerged to detect weak periodic signals immersed in noise. (–) Specifically, due to the advantages of immunity to strong backgrounds of zero‐mean probability distributions and high selectivity to a specific frequency, Duffing oscillators have been extensively used in the detection of amplitude, frequency, or phase of weak periodic signals with a low SNR. (–)…”

Section: Introductionmentioning

confidence: 99%

Adaptive time‐frequency representation for weak chirp signals based on Duffing oscillator stopping oscillation system

Hou

Yan

et al. 2018

Adaptive Control & Signal

View full text Add to dashboard Cite

To investigate high-resolution time-frequency representations for any type of weak chirp signals with a very low signal-noise ratio, we revisit the inherent deficiencies of conventional Duffing oscillator detection methods and propose a novel Duffing oscillator stopping oscillation detection system. As a result, the detection of chirp signals can be successfully realized, and the influence of nondetection zones and critical thresholds on the detection accuracy is successfully eliminated. Furthermore, we propose an adaptive Duffing oscillator stopping oscillation detection method to measure the instantaneous frequency variation of a highly dynamic chirp signal within a large frequency range. The simulation results indicate that, compared with the conventional Duffing oscillator detection methods and the Choi-Williams distribution, the proposed method greatly expands the frequency detection range of a single Duffing oscillator and has a lower computing cost and effective real-time performance in detecting a high-precision weak chirp signal, which provides a new solution for the time-frequency representation of weak chirp signals at a lower signal-noise ration and reveals broad prospects for applications in engineering.

show abstract

Nonlinear vibration and of the Duffing oscillator to parametric excitation with time delay feedback

Cited by 34 publications

References 12 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

Parametric Excitation of Pre-Stressed Graphene Sheets under Magnetic Field: Nonlinear Vibration and Dynamic Instability

Adaptive time‐frequency representation for weak chirp signals based on Duffing oscillator stopping oscillation system

Contact Info

Product

Resources

About