MATHEMATICAL MODEL OF NON-STSTIONARY THERMO-ELASTIC DEFORMATION OF MULTYLAYER DAMPHING COATINGS IN ELECTRONICS

Authors

  • Y. V. Mastinovskiy Zaporozhye National Technical University, Zaporozhye, Ukraine

DOI:

https://doi.org/10.15588/1607-3274-2015-4-2

Keywords:

magnetic field, thermo-elasticity, damping coatings, stresses, method of characteristics.

Abstract

Generation of new multilayer coatings of units and blocks in electronics for effective damping of thermo-mechanical impact loads requires the
development of mathematical models suitable for engineering practice. Mathematical model and calculation method proposed in this paper allows investigate the passing and reflection of thermo-elastic waves in a multilayer body excited by non-stationary magnetic field at the conductive layer boundary. Also, the problem of estimating relative influence of volume forces induced by the magnetic field in the electrically conductive nonferromagnetic layer on the wave propagation in thermo-elastic polymer compounds was considered. It is assumed that the velocity of heat propagation is finite. Assumptions are introduced to simplify the fully coupled system of magneto-thermo-elastic equations that allow applying the numerical solution based on the method of characteristics for obtaining concrete results. A method for finding required quantities at the nodal points of the boundary between the layers is indicated. The suggested mathematical model and calculation method makes it possible, without making any significant changes in the computing system, to carry out numerical experiments on researching the damping properties of multilayer
coatings with different geometrical and mechanical parameters under the conditions of the thermo-mechanical loadings. This calculation method of heterogeneous multilayer thermo-elastic structures can be used to identify the areas most disposed to the damage.

References

Партон В. З. Методы математической теории упругости / В. З. Партон, П. И. Перлин. – М. : Наука. Главн. ред. физ.- матем. лит., 1981. – 588 с. 2. Селезов И. Т. Нестационарные и нелинейные волны в электропроводящих средах / И. Т. Селезов, С. В. Корсунский. – Киев : Наукова думка, 1991. – 200 с. 3. Шамровский А. Д. Термоупругие волны и скорость их распространения в динамической задаче взаимосвязанной термоупругости / А. Д. Шамровский, Г. В. Меркотян // Восточно-Европейский журнал передовых технологий. – 2011. – Выпуск № 7 (53), том 5. – С. 41–45. 4. Bala Kiran. A Review of Two-Temperature Thermo-Еlasticity / Kiran Bala // International Journal of Modern Engineering Research (IJMER). – 2012. – Vol. 2, Issue 6.– pp. 4224–4227. 5. Moon F. C. Magnetically induced stress waves in a conducting solid – theory and experiment / F. C. Moon, S. Chattopadhyay // Transactions of the ASME. – 1974. – 41, Ser. E, № 3. – P. 641–646. 6. El-Bary A. A. Numerical Solution of Electro-magneto-thermomechanic Shock Problem / A. A. El-Bary // Commutational Methods in Science and Technology. – 2006. – Vol. 12 (2) – pp. 101–108. 7. Ezzat M. Generalized magneto-thermo-elasticity in a perfectly conducting mediem / M. Ezzat, H. Youssef // International Journal of Solids and Structures. – 2005. – Vol. 42. – pp. 6319–6334. 8. Коваленко А. Д. Термоупругость. / А. Д. Коваленко // Киев : Вища школа, 1975. – 216 с. 9. Беляев Н. М. Методы теории теплопроводности. В 2-х частях. / Н. М. Беляев, А. А. Рядно. Ч. 1. – М. : Высш. школа, 1982. – 237 с. 10. Сагамонян А. Я. Волны напряжений в сплошных средах / А. Я. Сагамонян // М.: Изд-во МГУ – 1985 – 416 с. 11. Chou P. C. A Unified Approach One-Dimensional Elastic Waves by the Method of Characteristics / P. C. Chou, R. W. Mortimer // Journal of Applied Mechanics. – 1967. – Vol. 34, No. 3 – pp. 745–750. 12. Данильченко Д. В. Нестационарные волны в составной цилиндрической оболочке / Д. В. Данильченко, Ю. В. Мастиновский // Нові матеріали і технології в металургії та машинобудуванні. – 2004. – № 1. – С. 105–107.

Published

2015-10-25

How to Cite

Mastinovskiy, Y. V. (2015). MATHEMATICAL MODEL OF NON-STSTIONARY THERMO-ELASTIC DEFORMATION OF MULTYLAYER DAMPHING COATINGS IN ELECTRONICS. Radio Electronics, Computer Science, Control, (4). https://doi.org/10.15588/1607-3274-2015-4-2

Issue

Section

Mathematical and computer modelling