Experimental evaluation of viscous damping coefficient in the fractional underdamped oscillator

Escalante-Martínez, J. E.; Gómez-Aguilar, J. F.; Calderón-Ramón, C.; Morales-Mendoza, Luis J.; Cruz-Orduña, Ines; Laguna-Camacho, J.R.

doi:10.1177/1687814016643068

Cited by 30 publications

(13 citation statements)

References 36 publications

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“…This fractional equation could give better experimental results for the current density in metals, due to the parameter 0 < ≤ 1 [49]- [51]. Recall that, in principle, we assume that the materials are homogeneous and isotropic, however, this is only the case under certain conditions.…”

Section: Fractional Drude Models With Caputo-fabrizio Derivativementioning

confidence: 99%

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Analysis of Drude model using fractional derivatives without singular kernels

et al. 2017

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Abstract:We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF), and fractional derivatives with a stretched Mittag-Le er function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < ≤ 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when < 0.8.

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Section: Fractional Drude Models With Caputo-fabrizio Derivativementioning

confidence: 99%

“…Motivated by recent experimental results [49][50][51] showing that simple models are best described by fractional differential equations, in [52] the fractional Caputo derivative is applied to study of the Drude model. However, as was mentioned above, this definition of the derivative has a singular kernel and cannot accurately describe the full memory effect.…”

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confidence: 99%

Analysis of Drude model using fractional derivatives without singular kernels

et al. 2017

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“…Also, dynamic responses of fractionally damped spring mass system have been investigated by Chakraverty and Behera (2013). Very recently, Escalante-Martínez et al (2016) have presented theoretical as well as experimental approach to find the viscous damping coefficient in the spring-mass viscodamper system. There, the authors have analysed the nonlocal damping model considering fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

Uncertain dynamic responses of imprecisely defined arbitrary order fractionally damped beam subject to various loads

Behera

Huang

Tapaswini

2018

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Purpose Recently, fractional differential equations have been used to model various physical and engineering problems. One may need a reliable and efficient numerical technique for the solution of these types of differential equations, as sometimes it is not easy to get the analytical solution. However, in general, in the existing investigations, involved parameters and variables are defined exactly, whereas in actual practice it may contain uncertainty because of error in observations, maintenance induced error, etc. Therefore, the purpose of this paper is to find the dynamic response of fractionally damped beam approximately under fuzzy and interval uncertainty. Design/methodology/approach Here, a semi analytical approach, variational iteration method (VIM), has been considered for the solution. A newly developed form of fuzzy numbers known as double parametric form has been applied to model the uncertainty involved in the system parameters and variables. Findings VIM has been successfully implemented along with double parametric form of fuzzy number to find the uncertain dynamic responses of the fractionally damped beam. The advantage of this approach is that the solution can be written in power series or compact form. Also, this method converges rapidly to have the accurate solution. The uncertain responses subject to impulse and step loads have also been computed and the behaviours of the responses are analysed. Applying the double parametric form, it reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches. Originality/value Uncertain dynamic responses of fuzzy fractionally damped beam using the newly developed double parametric form of fuzzy numbers subject to unit step and impulse loads have been obtained. Gaussian fuzzy numbers are used to model the uncertainties. In the methodology using the alpha cut form, corresponding beam equation is first converted to an interval-based fuzzy equation. Next, it has been transformed to crisp form by applying double parametric form of fuzzy numbers. Finally, VIM has been applied to solve the same for the general fuzzy responses. Various numerical examples have been taken in to consideration.

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“…In the recent decades, fractional calculus is found to be an excellent mathematical instrument to characterize viscoelastic behaviors [13][14][15][16][17][18][19][20] with fewer parameters. GWS Blair 21 proposed a viscoelastic model to connect the ideal Hookean and Newtonian components via the fractional derivative approach, called the Abel dashpot.…”

Section: Introductionmentioning

confidence: 99%

Characterizing the rheological behaviors of non-Newtonian fluid via a viscoelastic component: Fractal dashpot

Chen

2017

Advances in Mechanical Engineering

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Based on the fractal derivative, a robust viscoelastic element-fractal dashpot-is proposed to characterize the rheological behaviors of non-Newtonian fluid. The mechanical responses of the fractal dashpot are investigated with different strains and stresses, which are compared with the existing dashpot models, including the Newton dashpot and the Abel dashpot. The results show that as the derivative order is between 0 and 1, the viscoelastic behavior of the fractal dashpot is similar to that of the Abel dashpot. However, the fractal dashpot has a high computational efficiency compared with the Abel dashpot. On the other hand, the fractal dashpot can be reduced to the Newton dashpot when the derivative order equals to 1. As an extension of fractal dashpot, a fractal Bingham model is also introduced in this study. The accuracy of proposed fractal models is verified by the relevant rheological experimental data. Moreover, the obtained parameters can not only provide quantitative insights into both the viscoelasticity and the relative strength of rheopexy and thixotropy, but also quantitatively distinguish shear thinning and thickening phenomena.

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Experimental evaluation of viscous damping coefficient in the fractional underdamped oscillator

Cited by 30 publications

References 36 publications

Analysis of Drude model using fractional derivatives without singular kernels

Analysis of Drude model using fractional derivatives without singular kernels

Uncertain dynamic responses of imprecisely defined arbitrary order fractionally damped beam subject to various loads

Characterizing the rheological behaviors of non-Newtonian fluid via a viscoelastic component: Fractal dashpot

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