On a Ssystem of Coupled Linear Oscillators with Fractional Friction and Non-Constant Coefficients for Describing Geoacoustic Emission

Abstract

The paper proposes a generalization of the previously obtained mathematical model of geoacoustic emission, according to which the model takes into account the effects of heredity in dissipative terms. The model is a system of two coupled linear oscillators with non-constant coefficients and with fractional derivatives of Gerasimov-Caputo orders, which describe viscous friction (fractional friction). The mathematical model is studied numerically using a non-local explicit finite-difference scheme of the first order of accuracy, which was implemented in the Maple 2022 computer symbolic mathematics environment. In this computer environment, the modeling results were visualized: oscillograms and phase trajectories were constructed for different values of the model parameters. The interpretation of the modeling results is given. It is shown that fractional friction can affect the process of interaction of geoacoustic emission sources.

Keywords

• геоакустическая эмиссия
• дробная производная герасимова-капуто
• модель
• осциллограммы
• фазовая траектория
• maple 2022
• geoacoustic emission
• gerasimov-caputo fractional derivative
• model
• oscillograms
• phase trajectory
• maple 2022