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Harmonic waves of oscillation in different rocks using MathCAD modeling
Bakhyt Alipova

Last modified: 2023-05-15


Wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass transport. They consist, instead, of oscillations or vibrations around almost fixed locations. Waves are described by a wave equation which sets out how the disturbance proceeds over time. The mathematical form of this equation varies depending on the type of wave. Here we are using the system of coupled thermoelastodynamics in 2D (equation of motion and heat transfer). Here we have modeled speeds of longitudinal and transversal waves for different rocks as granite, shale, silicified shales, sandstone and siltstone. Characteristics of waves are investigated (amplitude, frequence, length of wave, period etc). Validity of the received results and their reliability is provided to that all theoretical ratios are received on the basis of use of rigorous mathematical research techniques, and numerical experiments in MathCAD were carried out when testing results on known decisions for elastic mediums.

Summing up results, concerning to the thermoelastic environment, the conclusion of results to each mountain breed is drawn. And also, these results and schedules will allow considerably will increase effectiveness at earth drillings, at creation of tunnels underground or at underground construction buildings.