MATHEMATICAL MODEL OF NON-STSTIONARY THERMO-ELASTIC DEFORMATION OF MULTYLAYER DAMPHING COATINGS IN ELECTRONICS
DOI:
https://doi.org/10.15588/1607-3274-2015-4-2Keywords:
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 thedevelopment 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.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2016 Y. V. Mastinovskiy
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Creative Commons Licensing Notifications in the Copyright Notices
The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.
The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.
The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.
Authors who publish with this journal agree to the following terms:
-
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
-
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
-
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.