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

Motchongom, M. T.; Tanekou, G. B.; Fozin, Fonzin; Kagho, L.Y.; Kengne, Romanic; Pelap, F. B.; Kofané, Timoléon Crépin

doi:10.1016/j.csfx.2021.100064

Cited by 5 publications

(6 citation statements)

References 40 publications

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“…Introducing the fractional friction and, fractional damping [25,26] and time the time delay, the equation of motion can now be rewritten as…”

Section: Model and Equation Of Motionmentioning

confidence: 99%

“…( ) D u r i t is the r-order derivative of ( ) u i t to t with the fractional order r. The parameters b and e can change respect to time. In this work we choose the perturbation parameters ( ) b t and ( ) e t as a form [24,25,30]: b e and w represent the constant oscillation amplitudes and the angular frequency, respectively.…”

Section: Model and Equation Of Motionmentioning

confidence: 99%

“…With the following property of sequential fractional derivatives [32]. 4) can be transformed into state equations by augmenting the forced system with ordinaries differentials equations which have an oscillatory solution of the form required for the forcing [25], which are given by (…”

Section: Numerical Explorationmentioning

confidence: 99%

“…The models used in these works are based on integer derivatives. Nevertheless, all these studies did not treat the problem of the frequency response on the spring-block model, except from our previous work, where we studied the effects of the fractional-order derivative and the stress perturbation on the dynamic of spring-block model [24,25]. In our previous study [25], we did not take in to account the impact of time delay on the shear stress frequency response.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, all these studies did not treat the problem of the frequency response on the spring-block model, except from our previous work, where we studied the effects of the fractional-order derivative and the stress perturbation on the dynamic of spring-block model [24,25]. In our previous study [25], we did not take in to account the impact of time delay on the shear stress frequency response. In present paper, we analyze the shear stress response and the transition between inter-seismic and coseismic periods of an earthquake considering the fractional-order viscous damping and delayed interaction between the blocks.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Delayed and fractional-order dynamics of a model for earthquake induced by stress perturbations

Bisong,

Mofor,

Fomekong

et al. 2024

Phys. Scr.

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Fractional calculus and time delay provide a powerful tool to model complex systems with memory, fractal systems and viscoelastic systems. Earthquakes are both complex systems with long-memory and some of their faults have fractal properties and, the rocks constituting faults have viscoelastic behavior. In this paper, we examined the dynamics of the spring-block considering the fractional viscous damping force and interaction between the blocks. The shear stress response is studied using the harmonic balance method and the numerical simulations are performed through Adams-Bashforth-Moulton scheme. The effects of the fractional-order and time delay on the amplitude-frequency curves and on the transition between steady state and seismic regime are investigated. The system response shows the existence of the resonance and anti-resonance. It appears that the resonance amplitude and resonance frequency are strongly dependent on the time delay and fractional-order. This resonance phenomenon results in an accumulation of energy which can lead to the destabilization of the fault system. At the anti-resonance the system response has minimum amplitude, and the blocks move without accumulated energy. The results show that the delay and fractional viscous can affect the properties of the rock, which is characterized by the modified linear stiffness coefficient, modified linear damping coefficient and the modified linear friction coefficient. The stability and hopf bifurcation are investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. The transition from stationary state to the periodic orbit and vice-versa through the hopf bifurcation is observed in the system.

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“…Introducing the fractional friction and, fractional damping [25,26] and time the time delay, the equation of motion can now be rewritten as…”

Section: Model and Equation Of Motionmentioning

confidence: 99%

Section: Model and Equation Of Motionmentioning

confidence: 99%

Section: Numerical Explorationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Delayed and fractional-order dynamics of a model for earthquake induced by stress perturbations

Bisong,

Mofor,

Fomekong

et al. 2024

Phys. Scr.

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Hopf bifurcation in fractional two-stage Colpitts oscillator: analytical and numerical investigations

Njoya

Kengne

Razafimandimby

et al. 2022

Int. J. Dynam. Control

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Energy function and complex dynamics from a jerk system

Yu,

Njitacke,

Jiang

et al. 2023

Phys. Scr.

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Jerk, as a mathematical concept, is used in mechanics to describe the rate of change of acceleration and plays a crucial role in the design of control systems for machines and vehicles. Therefore, it is important to master the various states and the energy released during the change of acceleration. This is why a new simple jerk function introduced afterward, energy released, is derived from a Hamilton function using the Helmholtz theorem. The condition of having a stable or unstable rate of change of acceleration is established using Hopf bifurcation theory. Some two-parameter stability charts are then computed for a suitable selection region of the study. Using some nonlinear analysis metrics, in the unstable region of the study, the occurrence of phenomena is found, such as reverse period doubling bifurcation, antimonotonicity, and hysteresis involving the coexistence of the states in the considered jerk system. An electronic circuit is built and used to implement the mathematical expression of the jerk equation and validate the result of the theoretical investigation.

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

Cited by 5 publications

References 40 publications

Delayed and fractional-order dynamics of a model for earthquake induced by stress perturbations

Delayed and fractional-order dynamics of a model for earthquake induced by stress perturbations

Hopf bifurcation in fractional two-stage Colpitts oscillator: analytical and numerical investigations

Energy function and complex dynamics from a jerk system

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