Non-linear problems of fractional calculus in modeling of mechanical systems

Grzesikiewicz, W.; Wakulicz, Andrzej; Zbiciak, Artur

doi:10.1016/j.ijmecsci.2013.02.007

Cited by 67 publications

(42 citation statements)

References 11 publications

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“…More complex behaviour may be obtained by enriching the creep function by additional terms (Podlubny 1999;Mainardi 2010;Grzesikiewicz et al 2013;Zbiciak 2013). Equations (6) and (7) are the starting points to characterize the viscoelastic properties of materials.…”

Section: Fractional Linear Viscoelastic Modelmentioning

confidence: 99%

Linear and Nonlinear Fractional Hereditary Constitutive Laws of Asphalt Mixtures

Mino

Airey

Paola

et al. 2016

Journal of Civil Engineering and Management

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Abstract. The aim of this paper is to propose a fractional viscoelastic and viscoplastic model of asphalt mixtures using experimental data of several tests such as creep and creep recovery performed at different temperatures and at different stress levels. From a best fitting procedure it is shown that both the creep one and recovery curve follow a power law model. It is shown that the suitable model for asphalt mixtures is a dashpot and a fractional element arranged in series. The proposed model is also available outside of the linear domain but in this case the parameters of the model depend on the stress level.

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Section: Fractional Linear Viscoelastic Modelmentioning

confidence: 99%

Linear and Nonlinear Fractional Hereditary Constitutive Laws of Asphalt Mixtures

Mino

Airey

Paola

et al. 2016

Journal of Civil Engineering and Management

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“…in which is Young's modulus, is the nonlocal characteristic parameter, is shear modulus, is viscoelastic damping coefficient and fractional derivative is also defined as [28] ( )…”

Section: Derivation Of Equationsmentioning

confidence: 99%

Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory

Ansari

Oskouie

Sadeghi

et al. 2015

Physica E: Low-dimensional Systems and Nanostructures

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“…It would be possible to use the same methodology in case of multi degree of freedom linear models representing rail track system with resilient elements. In such systems, half degrees of freedom can be associated with more general models of vibroacoustic elements, described by fractional-order derivatives [6], as it was suggested in [15]. Such an approach would make possible to fit better experimental results.…”

Section: Discussionmentioning

confidence: 99%

Mechanical modelling and application of vibroacoustic isolators in railway tracks

et al. 2017

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Abstract. The paper presents systematization and description of vibroacoustic isolators used in railway tracks (due to track structure type), with special attention paid to resilient mats. As in the second part of the paper the state-space mechanical model of a system with Under-Ballast Mat is formulated. Also some numerical problems arising from the mass matrix singularity are discussed. The poles of the system were calculated by using Matlab. Moreover, the influence of various parameters on the system's insertion loss and its transmissibility was visualized in figures.

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Non-linear problems of fractional calculus in modeling of mechanical systems

Cited by 67 publications

References 11 publications

Linear and Nonlinear Fractional Hereditary Constitutive Laws of Asphalt Mixtures

Linear and Nonlinear Fractional Hereditary Constitutive Laws of Asphalt Mixtures

Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory

Mechanical modelling and application of vibroacoustic isolators in railway tracks

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