Accounting for the friction in the contact area with oscillation of a rigid punch on surface a semi-infinite medium

Authors

  • Belyak O.A. Rostov State Transport University, Rostov-on-Don, Russian Federation
  • Suvorova T.V. Rostov State Transport University, Rostov-on-Don, Russian Federation

UDC

539.3

EDN

UOIUCE

DOI:

10.31429/vestnik-16-3-33-39

Abstract

The dynamic contact problem of oscillation of a rigid punch on a semi-infinite viscoelastic base is considered, moreover, friction in the contact area is taken into account. The base is provided with a microstructure wich is determinated in the framework of the micromechanics model. The problem is considered in a flat formulation for a steady-state oscillation regime. The base is modeled by a viscoelastic half-space. A rigid punch oscillates on the day surface of the elastic half-space. Normal and tangential stresses in the contact area are related by the Amonton-Coulomb law. Displacements satisfy the Lamaet equations. The connection of displacements and stresses is given by the generalized Hooke's law. The solution of this boundary value problem is constructed using the Fourier transform, which is applied to the Lamaet equations and boundary conditions. The base microstructure was taken into account in the framework of the micromechanics model. Mechanical characteristics corresponding to an equivalent elastic medium have been determined. The boundary-value problem is reduced to an integral equation of the first kind with a difference kernel. The numerical discretization of the integral equation is based on the collocation method. As a regularizer of the main part of the kernel, a function is used to isolate the logarithmic singularity, which coincides with it at infinity and has no singularities in the complex plane. As a result of discretization, the solution reduces to a finite system of equations with a quasi-diagonal matrix. The numerical analysis of the solution of the dynamic contact problem allowed us to draw the following conclusions. The change in contact stresses depending on the coefficient of friction in the contact region substantially depends on the oscillation frequency of the stamp. A significant effect on contact stresses is exerted by the coefficient of friction and the mechanical characteristics of the base material.

Keywords:

dynamic contact problem, friction and oscillation in contact domain

Funding information

Работа выполнена при поддержке РФФИ (проект 18-08-00260-а).

Authors info

  • Olga A. Belyak

    канд. физ.-мат. наук, доцент кафедры высшей математики Ростовского государственного университета путей сообщения

  • Tatyana V. Suvorova

    д-р физ.-мат. наук, профессор кафедры высшей математики Ростовского государственного университета путей сообщения

References

  1. Бабешко В.А., Евдокимова О.В., Бабешко О.М. Блочные элементы в контактных задачах с переменным коэффициентом трения// Докл. академии наук. 2018. Т. 480. № 5. С. 537–541. DOI: 10.7868/S0869565218050067 [Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M. Blochnyye elementy v kontaktnykh zadachakh s peremennym koeffitsiyentom treniya [Block elements in contact problems with a variable friction coefficient]. Dokl. akademii nauk [Doklady Physics], 2018, vol. 63, no. 6., pp. 239–243. DOI: 10.7868/S0869565218050067 (In Russian)]
  2. Бабешко В.А., Глушков Е.В., Зинченко Ж.Ф. Динамика неоднородных линейно-упругих сред. М.: Наука, 1989. 344 с. [Babeshko, V.A., Glushkov, E.V., Zinchenko, J.F. Dinamika neodnorodnykh lineyno-uprugikh sred [Dynamics of heterogeneous linearly elastic media]. Nauka Publ., Moscow, 1989. (In Russian)]
  3. Калинчук В.В., Белянкова Т.И. Динамические контактные задачи для предварительно напряженных тел. М.: Физматлит, 2002. 240 с. [Kalinchuk, V.V., Belyankova, T.I. Dinamicheskiye kontaktnyye zadachi dlya predvaritel'no napryazhennykh tel [Dynamic contact tasks for prestressed bodies]. Fizmatlit Publ., Moscow, 2002. (In Russian)]
  4. Горячева И.Г. Механика фрикционного взаимодействия. М.: Наука, 2001. 480 с. [Goryacheva I.G. Mekhanika friktsionnogo vzaimodeystviya [The mechanics of frictional interaction]. Moscow: Nauka Publ., 2001. (In Russian)]
  5. Горячева И.Г., Маховская Ю.Ю., Морозов А.В., Степанов Ф.И. Трение эластомеров. М.-Ижевск: Ин-т компьютерных исследований, 2017. 204 с. [Goryacheva, I.G. Makhovskaya, Yu.Yu., Morozov, A.V., Stepanov, F.I. Treniye elastomerov [Friction of elastomers]. Institute of Computer Research Publ., Moscow, Izhevsk, 2017. (In Russian)]
  6. Беляк О.А., Суворова Т.В. Влияние микроструктуры основания на силы трения при движении плоского штампа// Экологический вестник научных центров Черноморского экономического сотрудничества. 2018. № 3. С. 25–31. [Belyak, O.A., Suvorova, T.V. Vliyaniye mikrostruktury osnovaniya na sily treniya pri dvizhenii ploskogo shtampa [The influence of the base microstructure on the friction forces during the movement of a flat punch]. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva [Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation], 2018, no. 3, pp. 25–31. (In Russian)]
  7. Беляк О. А., Суворова Т.В., Усошин С.А. Волновое поле, генерируемое в слоистом пористоупругом полупространстве движущейся осциллирующей нагрузкой // Экологический вестник научных центров Черноморского экономического сотрудничества. 2008. № 1. С. 53–61. [Belyak, O.A., Suvorova, T.V., Usoshin, S.A. Volnovoye pole, generiruyemoye v sloistom poristouprugom poluprostranstve dvizhushcheysya ostsilliruyushchey nagruzkoy [The wave field generated in a layered porous-elastic half-space by a moving oscillating load]. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva [Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation], 2008, no. 1, pp. 53–61. (In Russian)]
  8. Беляк О.А., Суворова Т.В., Усошина Е.А. Математическое моделирование задачи о динамическом воздействии массивного объекта на неоднородное гетерогенное основание // Экологический вестник научных центров Черноморского экономического сотрудничества. 2014. № 1. С. 93–99. [Belyak, O.A., Suvorova, T.V., Usoshina, E.A. Matematicheskoye modelirovaniye zadachi o dinamicheskom vozdeystvii massivnogo obyekta na neodnorodnoye geterogennoye osnovaniye [Mathematical modeling of the dynamic impact of a massive object on a heterogeneous heterogeneous foundation]. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva [Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation], 2014, no 1, pp. 93–99. (In Russian)]
  9. Брычков Ю.А., Прудников А.П. Интегральные преобразования обобщенных функци. М.: Наука, 1977. 288 с. [Brychkov, Yu.A., Prudnikov, A.P. Integralnyye preobrazovaniya obobshchennykh funktsiy [Integral transformations of generalized functions. Nauka Publ., Moscow, 1977. (In Russian)]
  10. Бейтмен Г., Эрдейи А. Высшие трансцендентные функции. Т. 2. М.: Наука, 1974. 296 с. [Bateman, G., Erdeyi, A. Higher transcendental functions, vol. I–III. McGraw-Hill Book Company, New York, 1953.]
  11. Янке Е., Эмде Ф., Лёш Ф. Специальные функции. М.: Наука, 1964. 344 с. [Janke E., Emde F., Lesch F. Spetsialnyye funktsii [Special functions]. Nauka Publ., Moscow, 1964. (In Russian)]
  12. Иваночкин П.Г., Суворова Т.В., Данильченко С.А., Новиков Е.С., Беляк О.А. Комплексное исследование полимерных композитов с матрицей на основе фенилона С-2 // Вестник РГУПС. 2018. № 4. С. 54–62. [Ivanochkin, P.G., Suvorova, T.V., Danilchenko, S.A., Novikov, E.S., Belyak, O.A. Kompleksnoye issledovaniye polimernykh kompozitov s matritsey na osnove fenilona C-2 [A comprehensive study of polymer composites with a matrix based on phenylone C-2]. Vestnik Rostovskogo gosudarstvennogo universiteta putey soobshcheniya [Bulletin of RGUPS], 2018, no. 4, pp. 54–62. (In Russian)]
  13. Беляк О.А. Математические модели для определения механических свойств флюидосодержащих композитов // XII Всероссийский съезд по фундаментальным проблемам теоретической и прикладной механики: Ан. докл. Уфа, 2019. С. 247. [Belyak O.A. Matematicheskie modeli dlya opredeleniya mekhanicheskikh svoystv flyuidosoderzhashchikh kompozitov [Mathematical models for determining the mechanical properties of fluid-containing composites]. In: XII Vserossiyskiy s"ezd po fundamental'nym problemam teoreticheskoy i prikladnoy mekhaniki: Analiticheskiy doklad [XII All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics: An analytical report]. Ufa, 2019, pp. 247. (In Russian)]
  14. Кристенсен Р. Введение в механику композитов. М.: Мир, 1982. 335 с. [Christensen R.M. Mechanics of composite materials. Wiley, New York, 1979.]
  15. Giraud A., Huynh Q.V., Hoxha D., Kondo D. Effective poroelastic properties of transversely isotropic rock-like composites with arbitrarily oriented ellipsoidal inclusions// Mechanics of Materials.2007. Vol. 39. P. 1006–1024. DOI: 10.1016/j.mechmat.2007.05.005

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Issue

Vol. 16 (2019) No. 3

Pages

33-39

Section

Mechanics

Dates

Submitted

September 19, 2019

Accepted

September 23, 2019

Published

September 30, 2019

How to Cite

[1]
Belyak, O.A., Suvorova, T.V., Accounting for the friction in the contact area with oscillation of a rigid punch on surface a semi-infinite medium. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2019, т. 16, № 3, pp. 33–39. DOI: 10.31429/vestnik-16-3-33-39

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Copyright (c) 2019 Беляк О.А., Суворова Т.В.

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