DYNAMICS OF A THERMOELASTIC ROD UNDER UNSTEADY THERMAL AND FORCE INFLUENCES

СТАЦИОНАРЛЫҚ ЕМЕС ЖЫЛУ МЕН КҮШ ӘСЕРІНДЕГІ ТЕРМОҚАТТЫ ӨЗЕК ДИНАМИКАСЫ
ДИНАМИКА ТЕРМОУПРУГОГО СТЕРЖНЯ ПРИ НЕСТАЦИОНАРНЫХ ТЕПЛОВЫХ И СИЛОВЫХ ВОЗДЕЙСТВИЯХ
Ainakeyeva N.Zh.
2024 Kazakh-British Technical University

Herald of the Kazakh British Technical UNiversity
2024 #21 Issue 2 181 - 192 pp.

Rod elements are extensively utilized in various technological fields. An unsteady temperature field induces a time-varying stress field within the rod structure, impacting its strength and reliability during operation. Determining the thermally stressed state of rod structures, considering their mechanical properties (especially elasticity), is a significant scientific and technical challenge. The application of mathematical modeling methods enables the study of thermodynamic processes occurring within a structure and its elements, allowing for the determination of their dynamic and strength characteristics during the design phase. This paper addresses the Cauchy problem for the dynamics of a thermoelastic rod under arbitrary initial conditions and subjected to force and thermal influences. By employing the Green’s tensor for thermoelasticity equations, an analytical solution is derived, which determines deformations, stresses, and temperatures at any point along the rod at any given time, provided the initial state and the acting force and heat sources are known. Numerical calculations of temperature and displacement are presented for cases involving pulsed concentrated force and heat sources. Additionally, solutions to Cauchy problems under the influence of regular force and heat sources distributed along the rod are computed. The developed program allows for the investigation of thermodynamic processes in rods with various physical and mechanical properties, under the influence of both distributed and concentrated pulsed thermal and force sources, described by singular generalized functions.

Cauchy problem , displacement and stress , method of generalized functions , rod , temperature , uncouple thermoelasticity

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Joldasbekov Institute of Mechanics and Engeenering, Almaty, 050010, Kazakhstan
Kazakh National University named al-Farabi, Almaty, 050040, Kazakhstan
Narxoz University, Almaty, 050035, Kazakhstan

Joldasbekov Institute of Mechanics and Engeenering
Kazakh National University named al-Farabi
Narxoz University

10 лет помогаем публиковать статьи Международный издатель

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