Fractional dynamic of two-blocks model for earthquake induced by periodic stress perturbations

In this paper, the resonance behavior of a spring-block model with fractional-order derivative under periodic stress perturbation is investigated. Using the harmonic balance method, we derive the frequency-response equations for the system consisting of two blocks linked by a linear spring. The resu...

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Main Authors:	M.T. Motchongom, G.B. Tanekou, Fonzin Fozin, L.Y. Kagho, R. Kengne, F.B. Pelap, T.C. Kofane
Format:	Article
Language:	English
Published:	Elsevier 2021-12-01
Series:	Chaos, Solitons & Fractals: X
Subjects:	Fractional-order Resonance Anti-resonance Stress perturbation
Online Access:	http://www.sciencedirect.com/science/article/pii/S2590054421000099

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spelling	doaj-24140297bc924e8c83ce98c62e75df092021-09-23T04:40:25ZengElsevierChaos, Solitons & Fractals: X2590-05442021-12-017100064Fractional dynamic of two-blocks model for earthquake induced by periodic stress perturbationsM.T. Motchongom0G.B. Tanekou1Fonzin Fozin2L.Y. Kagho3R. Kengne4F.B. Pelap5T.C. Kofane6Higher Technical Teachers Training College, University of Bamenda, PO.Box 39 Bambili, CameroonUnity of Research of Mechanics and Modelling of Physical Systems, Department of physics, Faculty of Science, University of Dschang, PO Box 69 Dschang, Cameroon; Corresponding author at: University of Dschang Faculty of Sciences: Universite de Dschang Faculte des Sciences, Cameroon.Unity of Research of Condensed Matter, Electronic and signal processing, Department of physics, Faculty of Science, University of Dschang, PO Box 69 Dschang, Cameroon; Department of Electrical and Electronic Engineering, Faculty of Engineering and Technology (FET), University of Buea, P.O. Box 63, Buea, CameroonUnity of Research of Mechanics and Modelling of Physical Systems, Department of physics, Faculty of Science, University of Dschang, PO Box 69 Dschang, CameroonUnity of Research of Condensed Matter, Electronic and signal processing, Department of physics, Faculty of Science, University of Dschang, PO Box 69 Dschang, CameroonUnity of Research of Mechanics and Modelling of Physical Systems, Department of physics, Faculty of Science, University of Dschang, PO Box 69 Dschang, CameroonLaboratoire de Mecanique, Faculté des sciences, Université de Yaoundé I, BP 812, Yaoundé, CamerounIn this paper, the resonance behavior of a spring-block model with fractional-order derivative under periodic stress perturbation is investigated. Using the harmonic balance method, we derive the frequency-response equations for the system consisting of two blocks linked by a linear spring. The results have shown that the fractional-order derivative and perturbation parameter can affect the dynamical properties of fault rock, which is characterized by the equivalent linear damping coefficient and the equivalent linear stiffness coefficient. The frequency-response curve displays the resonance peaks and one anti-resonance. The effects of parameters q,β0,ε0,β1 and ε1on the resonance and anti-resonance periods and the response amplitudes at the resonance frequency are analyzed. The shear stress response shows that the system accumulates a lot of energy at the resonance frequency. This accumulation can lead to the destabilization of the fault system. The blocks move without accumulating energy at the anti-resonance frequency. This can lead to the stabilization of the fault system.http://www.sciencedirect.com/science/article/pii/S2590054421000099Fractional-orderResonanceAnti-resonanceStress perturbation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	M.T. Motchongom G.B. Tanekou Fonzin Fozin L.Y. Kagho R. Kengne F.B. Pelap T.C. Kofane
spellingShingle	M.T. Motchongom G.B. Tanekou Fonzin Fozin L.Y. Kagho R. Kengne F.B. Pelap T.C. Kofane Fractional dynamic of two-blocks model for earthquake induced by periodic stress perturbations Chaos, Solitons & Fractals: X Fractional-order Resonance Anti-resonance Stress perturbation
author_facet	M.T. Motchongom G.B. Tanekou Fonzin Fozin L.Y. Kagho R. Kengne F.B. Pelap T.C. Kofane
author_sort	M.T. Motchongom
title	Fractional dynamic of two-blocks model for earthquake induced by periodic stress perturbations
title_short	Fractional dynamic of two-blocks model for earthquake induced by periodic stress perturbations
title_full	Fractional dynamic of two-blocks model for earthquake induced by periodic stress perturbations
title_fullStr	Fractional dynamic of two-blocks model for earthquake induced by periodic stress perturbations
title_full_unstemmed	Fractional dynamic of two-blocks model for earthquake induced by periodic stress perturbations
title_sort	fractional dynamic of two-blocks model for earthquake induced by periodic stress perturbations
publisher	Elsevier
series	Chaos, Solitons & Fractals: X
issn	2590-0544
publishDate	2021-12-01
description	In this paper, the resonance behavior of a spring-block model with fractional-order derivative under periodic stress perturbation is investigated. Using the harmonic balance method, we derive the frequency-response equations for the system consisting of two blocks linked by a linear spring. The results have shown that the fractional-order derivative and perturbation parameter can affect the dynamical properties of fault rock, which is characterized by the equivalent linear damping coefficient and the equivalent linear stiffness coefficient. The frequency-response curve displays the resonance peaks and one anti-resonance. The effects of parameters q,β0,ε0,β1 and ε1on the resonance and anti-resonance periods and the response amplitudes at the resonance frequency are analyzed. The shear stress response shows that the system accumulates a lot of energy at the resonance frequency. This accumulation can lead to the destabilization of the fault system. The blocks move without accumulating energy at the anti-resonance frequency. This can lead to the stabilization of the fault system.
topic	Fractional-order Resonance Anti-resonance Stress perturbation
url	http://www.sciencedirect.com/science/article/pii/S2590054421000099
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Fractional dynamic of two-blocks model for earthquake induced by periodic stress perturbations

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