Contact problem on vibration of a punch on a microneogeneous viscoelastic base with consideration of friction in the contact region

Authors

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-20-4-6-10

Abstract

The paper considers the contact problem of vibration of a rigid punch with a plane base on a microneogeneous viscoelastic half-space when friction in the contact region is taken into account. The microheterogeneity of the medium is taken into account in the framework of the Biot-Frenkel multiphase medium model for porous-elastic fluid-saturated medium. The viscosity of the fluid filling the pores is taken into account and the skeleton is assumed to be viscoelastic. Rheological properties of the skeleton are taken into account in the framework of the concept of complex modules. The boundary value problem for the Biot medium is reduced to an integral equation of the first kind with a difference kernel with respect to normal contact pressures. The solution of the integral equation after regularization by feature extraction is realized numerically by the boundary element method. Numerical experiment has been carried out for the skeleton material, an epoxyphenolic resin modified with magnesium oxide, which contains cylinder oil in its pores. The viscoelastic skeleton is described within the framework of the standard viscoelastic body model with long modulus and instantaneous modulus and relaxation time. The dependence of contact stresses on the frequency oscillations has been investigated. On the basis of numerical experiments the range of frequencies has been established, for which it is shown that the account of friction in the contact area and viscosity of the matrix of heterogeneous medium has the greatest influence on the contact stresses.

Keywords:

dynamic contact problem, contact region friction, fluid-saturated porous medium, viscous elastic skeleton

Acknowledgement

The work was financially supported by the Russian Science Foundation (project No 21-19-00288).

Author Infos

Olga A. Belyak

д-р физ.-мат. наук, профессор кафедры "Теоретическая механика" Ростовского государственного университета путей сообщения

e-mail: o_bels@mail.ru

Tatyana V. Suvorova

д-р физ.-мат. наук, профессор кафедры "Высшая математика" Ростовского государственного университета путей сообщения

e-mail: suvorova_tv111@mail.ru

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. [Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M., Block elements in contact problems with a variable friction coefficient. Doklady akademii nauk = Rep. of the Academy of Sciences, 2018, vol. 480, no. 5, pp. 537–541. (in Russian)]
  2. Горячева, И.Г., Маховская, Ю.Ю., Морозов, А.В., Степанов, Ф.И., Трение эластомеров. Москва, Ижевск: Ин-т компьютерных исследований, 2017. [Goryacheva, I.G., Makhovskaya, Yu.Yu., Morozov, A.V., Stepanov, F.I., Trenie elastomerov = Friction of elastomers. Moscow-Izhevsk, Institute of Computer Research Publ., 2017. (in Russian)]
  3. Торская, Е.В., Модели фрикционного взаимодействия тел с покрытиями. Москва, Ижевск, Ин-т компьютерных исследований, 2020. [Torskaya, E.V., Modeli frikcionnogo vzaimodejstviya tel s pokrytiyami = Models of frictional interaction of bodies with coatings. Moscow, Izhevsk, Institute of Computer Research, 2020. (in Russian)]
  4. Колесников, В.И., Беляк, О.А., Математические модели и экспериментальные исследования –- основа конструирования гетерогенных антифрикционных материалов. Москва, Физматлит, 2021. [Kolesnikov, V.I., Belyak, O.A., Matematicheskie modeli i eksperimental'nye issledovaniya –- osnova konstruirovaniya geterogennyh antifrikcionnyh materialov = Mathematical models and experimental studies – the basis for the design of heterogeneous antifriction materials. Moscow, Fizmatlit, 2021. (in Russian)]
  5. Balci, M.N., Dag, S., Dynamic frictional contact problems involving elastic coating. Tribology International, 2018, vol. 124, pp. 70–92. DOI: 10.1016/J.TRIBOINT.2018.03.033
  6. Biot, M.A., Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics, 1962, vol. 33, no. 4, pp. 1482–1498.
  7. Perrot, C., Chevillotte, F., Hoang, M.T., Bonnet, G., Becot, F.-X., Gautron, L., Duval, A., Microstructure, transport, and acoustic properties of open-cell foam samples: Experiments and three-dimensional numerical simulations. J. Appl. Phys., 2012, vol. 111, 014911, DOI: 10.1063/1.3673523
  8. Becot, F.-X., Jaouen, L., An alternative Biot's formulation for dissipative porous media with skeleton deformation. J. Acoust. Soc. Am., 2013, vol. 134, no. 6, pp. 4801–4807. DOI: 10.1121/1.4826175
  9. Christensen, R.M., Mechanics of composite materials. New York, Wiley, 1979.
  10. Матвеенко, В.П., Сметанников, О.Ю., Труфанов, Н.А., Шардаков, И.Н., Термомеханика полимерных материалов в условиях релаксационного перехода. Москва, Физматлит, 2009. [Matveenko, V.P., Smetannikov, O.Ju., Trufanov, N.A., Shardakov, I.N., Termomekhanika polimernyh materialov v usloviyah relaksacionnogo perekhoda = Thermomechanics of polymeric materials under relaxation transition conditions. Moscow, Fizmatlit, 2009. (in Russian)]
  11. Сеймов, В.М., Трофимчук, А.Н., Савицкий, О.А., Колебания и волны в слоистых средах. Киев, Наук. думка, 1990. [Sejmov,V. M., Trofimchuk, A. N., Savickij, O. A., Kolebaniya i volny v sloistyh sredah = Oscillations and waves in layered media. Kiev, Nauk. dumka, 1990. (in Russian)]
  12. Ai, Z.Y., Zhao, Y.Z., Liu, W.J., Fractional derivative modeling for axisymmetric consolidation of multilayered cross-anisotropic viscoelastic porous media. Computers \& Mathematics with Applications, 2020, vol. 79, no. 5 pp. 1321-1334. DOI: 10.1016/j.camwa.2019.08.033
  13. Беляк, О.А., Суворова, Т.В., Учет трения в области контакта при колебаниях жесткого штампа на поверхности полуограниченной среды. Экологический вестник научных центров Черноморского экономического сотрудничества, 2019, т. 16, № 3, с. 33–39. [Belyak, O.A., Suvorova, T.V., Consideration of friction in the contact region at oscillations of a rigid die on the surface of a semi-confined medium. Ekologicheskij vestnik nauchnyh centrov Chernomorskogo ekonomicheskogo sotrudnichestva = Ecological Bulletin of the Scientific Centers of the Black Sea Economic Cooperation, 2019, vol. 16, no. 3, pp. 33–39. (in Russian)] EDN: UOIUCE
  14. Бребия, К., Теллес, Ж., Вроубел, Л., Методы граничных элементов. Москва, Мир, 1987. [Brebbia, K., Telles, G., Vroubel, L. Metody granichnyh elementov = Boundary Element Methods. Moscow, Mir, 1987. (in Russian)]
  15. Беляк, О.А., Суворова, Т.В., Колебания штампа на поверхности гетерогенного слоя при учете трения в области контакта. Прикладная математика и механика, 2021, т. 85, № 3, с. 321–331. [Belyak, O.A., Suvorova, T.V., vibrations of a punch on the surface of a heterogeneous layer with account of friction in the contact area. Prikladnaya matematika i mekhanika = Applied Mathematics and Mechanics, 2021, vol. 85, no. 3, pp. 321–331 (in Russian)]
  16. Kolesnikov, V.I., Suvorova, T.V., Belyak, O.A., Modeling antifriction properties of composite based on dynamic contact problem for a heterogeneous foundation. Materials Physics and Mechanics, 2020, vol. 46, pp. 139–148. DOI: 10.18720/MPM.4612020_14

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Issue

2023. Vol. 20. No. 4

Section

Mechanics

Pages

6-10

Submitted

2023-09-26

Published

2023-12-31

How to Cite

Belyak O.A., Suvorova T.V. Contact problem on vibration of a punch on a microneogeneous viscoelastic base with consideration of friction in the contact region. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2023, vol. 20, no. 4, pp. 6-10. DOI: https://doi.org/10.31429/vestnik-20-4-6-10 (In Russian)

Copyright (c) 2024 Belyak O.A., Suvorova T.V.

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