Solutions of coupled problem of thermomechanics for electroconductive hollow cylinder under non-stationary electromagnetic action
Date
2017-06-15
Journal Title
Journal ISSN
Volume Title
Publisher
Lviv Politechnic Publishing House
Abstract
Сформульовано плоску осесиметричну зв’язану динамiчну задачу термомеханiки для
електропровiдного порожнистого цилiндра за однорiдної нестацiонарної електрома-
гнiтної дiї. Для побудови ї ї розв’язку використано апроксимацiю визначальних фун-
кцiй осьової комппоненти вектора напруженостi магнiтного поля, температури та
радiальної компоненти вектора перемiщень за радiальною змiнною кубiчними по-
лiномами. У результатi вихiднi початково-крайовi задачi на визначальнi функцiї зве-
дено до задач Кошi за часовою змiнною на iнтегральнi характеристики цих функцiй.
Отримано вирази iнтегральних характеристик у виглядi згорток функцiй, що опи-
сують однорiднi розв’язки та заданi граничнi значення визначальних функцiй. Як
приклад числово проаналiзовано амплiтудно-частотнi характеристики радiальних на-
пружень у цьому цилiндрi за врахування зв’язностi полiв температури i перемiщень
i без такого врахування.
A plane axisymmetrical coupled dynamic problem of thermomechanics for an electroconductive hollow cylinder under homogeneous non-stationary electromagnetic action is formulated. To construct its solution, the approximation of the determining functions the axial component of the magnetic field strength vector, the temperature, and the radial component of the displacement vector with respect to the radial variable by cubic polynomials is used. As the result, the initial-boundary problem for determining functions is reduced to a Cauchy problem with respect to the time variable for the integral characteristics of these functions. The expressions of integral characteristics are obtained in the form of a convolution of functions describing the uniform solutions and the given limit values of determining functions. As an example, the amplitude-frequency characteristics of the radial stresses in the given cylinder are analyzed numerically, with taking into account the connectivity between the temperature and the displacement fields as well as without such accounting.
A plane axisymmetrical coupled dynamic problem of thermomechanics for an electroconductive hollow cylinder under homogeneous non-stationary electromagnetic action is formulated. To construct its solution, the approximation of the determining functions the axial component of the magnetic field strength vector, the temperature, and the radial component of the displacement vector with respect to the radial variable by cubic polynomials is used. As the result, the initial-boundary problem for determining functions is reduced to a Cauchy problem with respect to the time variable for the integral characteristics of these functions. The expressions of integral characteristics are obtained in the form of a convolution of functions describing the uniform solutions and the given limit values of determining functions. As an example, the amplitude-frequency characteristics of the radial stresses in the given cylinder are analyzed numerically, with taking into account the connectivity between the temperature and the displacement fields as well as without such accounting.
Description
Keywords
зв’язана задача термомеханіки, порожнистий електропровідний циліндр, нестаціонарна електромагнітна дія, апроксимація, інтегральні характеристики, coupled problem of thermomechanics, hollow electroconductive cylinder, nonstationary electromagnetic action, approximation, integral characteristics
Citation
Musij R. Solutions of coupled problem of thermomechanics for electroconductive hollow cylinder under non-stationary electromagnetic action / R. Musij, Kh. Drohomyretska, O. Oryshchyn // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 4. — No 1. — P. 69–77.