Mathematical model of the stick-slip effect for describing the “drumbeat” seismic regime during the eruption of the Kizimen volcano in Kamchatka

Parovik, Roman; Shakirova, A. A.; Фирстов, П. П.

doi:10.1063/5.0092351

Cited by 3 publications

(1 citation statement)

References 12 publications

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“…A concrete example of dry friction types in systems can be seen in recent research that applies to the flow of lava on an inclined surface, modelled as a stick-slip effect [19,20]. The mathematical approach used involves fractional derivatives, which allow for a generalisation of the stick-slip model.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Model of the Evolution of a Simple Dynamic System with Dry Friction

Alaci,

Ciornei,

Lupascu

et al. 2024

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A simple dynamic system with dry friction is studied theoretically and numerically. Models of systems including dry friction are not easily obtained, as defining the relationship between the friction force and the relative velocity presents a significant challenge. It is known that friction forces exhibit notable discontinuities when there is a change in the direction of motion. Additionally, when the relative motion ceases, the friction force can assume any value within a certain range. In the literature, numerous models of dry friction are presented, and most of them assume a biunivocal dependency of the friction force with respect to relative velocity. The dynamic system considered here is a tilted rod with spherical ends, initially at rest. Dry friction forces are evident at the contact point with the horizontal plane. The ball–plane contact highlights the rolling friction or/and sliding friction. The problem is theoretically solved after adopting one of the two cases of friction: rolling friction or sliding friction. The nonlinear differential equations of motion have been derived, along with expressions for the magnitude of the normal reaction and the friction force. The results of the model are displayed graphically for three different sets of values for the coefficient of friction. It is revealed that there is a critical value of the coefficient of friction that determines the transition from rolling to sliding regimes. To validate the theoretical model, dynamic simulation software was utilised. The excellent match between the theoretical predictions and the results from the numerical simulation confirms the accuracy of the proposed analytical solution.

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Section: Introductionmentioning

confidence: 99%

Mathematical Model of the Evolution of a Simple Dynamic System with Dry Friction

Alaci,

Ciornei,

Lupascu

et al. 2024

Axioms

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Multiplets of low-frequency earthquakes during the eruption of the Kizimen volcano in 2011–2012, Russia

Shakirova

Chemarev

2023

Journal of Volcanology and Geothermal Research

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Analytical model of small fluctuations of compressible magma with Maxwell rheology in the feeding system of a volcano. Part 1. Density oscillations

Radionoff

2023

Russian Journal of Earth Sciences

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The analytical mathematical model is presented that describes one of the possible mechanisms for the occurrence of long-period seismic events that are often recorded near active volcanic centers. The feeding system of the volcano is modeled in the simplest form of a cylindrical channel filled with a compressible magmatic melt with the rheology of a Maxwell body. It is shown that such a magmatic body can experience harmonic damped oscillations, the damping coefficient of which is determined by the relaxation time of the magmatic melt. These fluctuations may appear as a response to a density perturbation caused by the influx of denser magma from deep layers or a change in pressure in the supply system of the volcano. The dependence of the natural oscillatory frequency on the physical characteristics of the magmatic melt and the geometric dimensions of the feed channel is shown. When the compressibility of the magmatic melt is taken into account, density perturbations depend on the size of the feeding system and are characterized by periodic oscillations, which are most pronounced near the channel axis. Oscillations are also experienced by the flow velocity component directed along the radius of the cylinder. The source mechanism of the long-period seismic events is discussed. The model is used to describe long-period oscillations recorded near Santiaguito (Guatemala).

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Mathematical model of the stick-slip effect for describing the “drumbeat” seismic regime during the eruption of the Kizimen volcano in Kamchatka

Cited by 3 publications

References 12 publications

Mathematical Model of the Evolution of a Simple Dynamic System with Dry Friction

Mathematical Model of the Evolution of a Simple Dynamic System with Dry Friction

Multiplets of low-frequency earthquakes during the eruption of the Kizimen volcano in 2011–2012, Russia

Analytical model of small fluctuations of compressible magma with Maxwell rheology in the feeding system of a volcano. Part 1. Density oscillations

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