Fractional derivative and time delay damper characteristics in Duffing–van der Pol oscillators

Leung, A.Y.T.; Guo, Zhao; Yang, H.X.

doi:10.1016/j.cnsns.2013.02.013

Cited by 26 publications

(12 citation statements)

References 37 publications

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“…In Refs. [4,5], the periodic oscillation of the fractional order nonlinear systems is investigated via the residue harmonic balance method, and the effects of the fractional order and system parameter on the vibration frequency and amplitude are revealed.…”

Section: Introductionmentioning

confidence: 99%

Optimization analysis of Duffing oscillator with fractional derivatives

Liao

2014

Nonlinear Dyn

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The improved version of the constrained optimization harmonic balance method is presented to solve the Duffing oscillator with two kinds of fractional order derivative terms. The analytical gradients of the objective function and nonlinear quality constraints with respect to optimization variables are formulated and the sensitivity information of the Fourier coefficients can also obtained. A new stability analysis method based on the analytical formulation of the nonlinear equality constraints is presented for the nonlinear system with fractional order derivatives. Furthermore, the robust stability boundary of periodic solution can be determined by the interval eigenvalue problem. In addition, the sensitivity information mixed with the interval analysis method is used to quantify the response bounds of periodic solution. Numerical examples show that the proposed approach is valid and effective for analyzing fractional derivative nonlinear system in the presence of uncertainties. It is illustrated that the bifurcation solution in the fractional nonlinear systems may not be sensitive to the variation of the influence parameters.

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Section: Introductionmentioning

confidence: 99%

Optimization analysis of Duffing oscillator with fractional derivatives

Liao

2014

Nonlinear Dyn

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“…Of course the "classical" Ishlinsky-Prandtl converter is determined as a continuos system (sum should be replaced by an integral). However in our numerical simulations it is more appropriate to use the discrete analog of the Ishlinsky-Prandtl converter (7). In this way in the following consideration we will call the converter (7) as an Ishlinsky-Prandtl converter.…”

Section: Hysteretic Materialsmentioning

confidence: 99%

“…where W is an Ishlinsky-Prandtl operator which is determined by the relation (7). In this case the equation of motion for the considered system becomes:…”

Section: Hysteretic Dampingmentioning

confidence: 99%

“…One way to solve this problem is to use a nonlinear viscous damper [1][2][3][4][5] or damper with hysteretic properties. It should also be pointed out the exciting and interesting (generally, from the fundamental point of view) model of a e-mail: mkl150@mail.ru b e-mail: melechp@yandex.ru viscous damping which is based on the technique of fractional derivatives and can be called as a fractional damping [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Hysteretic damper based on the Ishlinsky-Prandtl model

et al. 2016

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“…The designed problem was ill-posed, and a regularization scheme is used to get faithful estimation of parameters. The nonlinear oscillators are well studied by many researchers for instant see [8][9][10][11][12][13][14][15][16] and references therein. A valuable investigation has been conducted to detect the parameters from noisy data for forced nonlinear oscillators [17][18][19][20][21][22][23][24] and provides base for the new exploration in area of inverse problems.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous detection of the nonlinear restoring and excitation of a forced nonlinear oscillation: an integral approach

et al. 2015

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We address in this article, how to calculate the restoring characteristic and the excitation of a nonlinear forced oscillating system. Under the assumption that the forced nonlinear oscillator has a periodic solution with period T = 2π/ω, we constructed a system of linear equations by introducing time-dependent multipliers. The periodicity assumption helps to simplify the system of linear equations. The stability and uniqueness are also presented for the inverse problem. Numerical testing is conducted to show the effectiveness of our presented methodology.

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Fractional derivative and time delay damper characteristics in Duffing–van der Pol oscillators

Cited by 26 publications

References 37 publications

Optimization analysis of Duffing oscillator with fractional derivatives

Optimization analysis of Duffing oscillator with fractional derivatives

Hysteretic damper based on the Ishlinsky-Prandtl model

Simultaneous detection of the nonlinear restoring and excitation of a forced nonlinear oscillation: an integral approach

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