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

DOI:

https://doi.org/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

Acknowledgement

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

Author Infos

Olga A. Belyak

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

e-mail: o_bels@mail.ru

Tatyana V. Suvorova

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

e-mail: suvorova_tv111@mail.ru

References

  1. 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. 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. 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. Goryacheva I.G. Mekhanika friktsionnogo vzaimodeystviya [The mechanics of frictional interaction]. Moscow: Nauka Publ., 2001. (In Russian)
  5. 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. 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. 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. 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. Brychkov, Yu.A., Prudnikov, A.P. Integralnyye preobrazovaniya obobshchennykh funktsiy [Integral transformations of generalized functions. Nauka Publ., Moscow, 1977. (In Russian)
  10. Bateman, G., Erdeyi, A. Higher transcendental functions, vol. I–III. McGraw-Hill Book Company, New York, 1953.
  11. Janke E., Emde F., Lesch F. Spetsialnyye funktsii [Special functions]. Nauka Publ., Moscow, 1964. (In Russian)
  12. 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. 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. 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, pp. 1006–1024. DOI: 10.1016/j.mechmat.2007.05.005

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Issue

2019. Vol. 16. No. 3

Section

Mechanics

Pages

33-39

Submitted

2019-09-19

Published

2019-09-30

How to Cite

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, vol. 16, no. 3, pp. 33-39. DOI: https://doi.org/10.31429/vestnik-16-3-33-39 (In Russian)

Copyright (c) 2019 Belyak O.A., Suvorova T.V.

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