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

• Published in: Chaos, Solitons & Fractals: X Vol. 7; p. 100064
• Main Authors: Motchongom, M.T., Tanekou, G.B., Fozin, Fonzin, Kagho, L.Y., Kengne, R., Pelap, F.B., Kofane, T.C.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.12.2021; Elsevier
• Subjects: Anti-resonance; Fractional-order; Resonance; Stress perturbation; Fractional-order; Resonance; Stress perturbation; Anti-resonance
• ISSN: 2590-0544; 2590-0544
• DOI: 10.1016/j.csfx.2021.100064

•Equivalent linear damping coefficient and equivalent linear stiffness in term of the fractional-order derivative and perturbations stress amplitude is established.•The effects of the fractional-order on the resonance and anti-resonance period are studied.•The shear stress response can be controlled by the stress perturbation. 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 ε1 on 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.