Full Article: PDF
Scientific Object Identifier: http://s-o-i.org/1.1/TAS-01-117-57
DOI: https://dx.doi.org/10.15863/TAS.2023.01.117.57
Language: Russian
Citation: Akhmedov, O. S. (2023). Investigation of the oscillation of an elastic rod in time taking into account the relaxation properties of materials. ISJ Theoretical & Applied Science, 01 (117), 672-677. Soi: http://s-o-i.org/1.1/TAS-01-117-57 Doi: https://dx.doi.org/10.15863/TAS.2023.01.117.57 |
Pages: 672-677
Published: 30.01.2023
Abstract: In the present work, a mathematical model of oscillations of an elastic rod under the action of an external harmonic load is developed, taking into account the relaxation properties of the material and the resistance forces exerted by the rod to the process of changing its shape. The differential equation of the model was obtained taking into account the time dependence of stresses and strains in the formula of Hooke's law, reduced to the form of complicated Maxwell and Kelvin-Voigt models. The results of studying the model by the numerical method allow us to conclude that when the frequency of natural oscillations of the rod coincides with the frequency of oscillations of the external load, a resonance is observed, accompanied by an unlimited increase in the oscillation amplitude (in the absence of medium resistance).
Key words: elastic deformation, rod oscillations, relaxation coefficient, drag coefficient, resonant vibrations.
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