Математичне моделювання та аналіз термопружної поведінки електропровідного циліндра з тонким електропровідним покриттям за імпульсної електромагнітної дії

• Дата: 2018
• Автори: Мусій, Роман Степанович, Мельник, Наталія Богданівна, Андрусяк, Іванна Володимирівна, Бродяк, Оксана Ярославівна, Гошко, Любомир Васильович
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: Kamianets-Podilskyi National Ivan Ohiienko University 2018
• Онлайн доступ: http://mcm-tech.kpnu.edu.ua/article/view/140046
• Назва журналу: Mathematical and computer modelling. Series: Technical sciences

A mathematical model for determination of the thermostressed state of a long integrate elecrtroconductive cylinder with a thin conductive coating is constructed and the evaluation criterion for its operability and properties preservation of contact connection depending on the parameters of the external electromagnetic action is proposed. A calculation model of the problem for the considered electroconductive cylinder consisting of three stages is selected. In the first stage, from the Maxwell relations the nonzero axial component of the magnetic field stress vector in the cylinder and in the coating and the corresponding to it specific densities of the Joule heat ejections and ponderomotive forces are determined. It the second stage, from the equation of the heat conductivity taking into account the known Joule heat ejections, the temperature distribution in the cylinder and in the coating are obtained. In the third stage, according to the known ponderomotive forces and temperature , from the relations of the plane axisymmetric problem of thermoelasticity in displacements, the radial component of the displacement vector and the radial, circle and axial components of the dynamic stresses tensor, as well as the intensity of the total stresses caused both by Joule heat and ponderomotor forces in the cylinder and coverings are determined. For solving the formulated initial-boundary value problems of thermomechanics, the method which is based on approximation of distributions of the determining functions (axial components of the magnetic field stress vector, temperature and radial component of the displacement vector) in the cylinder and in the cover by the quadratic polynomials in radial variable was propozed. This method has made it possible to reduce the initial-boundary value problems for the determining functions to the corresponding time Cauchy problems on the integral characteristics of these functions. The solutions of the considered thermoelasticity problem under the action of electromagnetic impulse were obtained and the computer analysis of the ponderomotive force, the temperature and the radial and circular stresses was done. The results of the analysis are illustrated by the graphs of time dependence of determining functions in the considered cylinder with a thin conductive coating.