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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Volume 281, Pages 98–126
DOI: https://doi.org/10.1134/S037196851302009X (Mi tm3467) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Ball on a viscoelastic plane

A. A. Zobovaa, D. V. Treschevb

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia
b Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
Full-text PDF (367 kB) Citations (9)
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DOI: https://doi.org/10.1134/S037196851302009X
Abstract: We consider dynamical problems arising in connection with the interaction of an absolutely rigid ball and a viscoelastic support plane. The support is a relatively stiff viscoelastic Kelvin–Voigt medium that coincides with the horizontal plane in the undeformed state. We also assume that under the deformation the support induces dry friction forces that are locally governed by the Coulomb law. We study the impact appearing when a ball falls on the plane. Another problem of our interest is the motion of a ball “along the plane”. A detailed analysis of various stages of the motion is presented. We also compare this model with classical models of interaction of solid bodies.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
Russian Foundation for Basic Research 12-01-31059
The work was supported by a grant of the Government of the Russian Federation (project no. 11.G34.31.0039) and in part by the Russian Foundation for Basic Research (project no. 12-01-31059).
Received in July 2012
English version:
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 281, Pages 91–118
DOI: https://doi.org/10.1134/S0081543813040093
Bibliographic databases:
Document Type: Article
UDC: 539.3
Language: Russian
Citation: A. A. Zobova, D. V. Treschev, “Ball on a viscoelastic plane”, Modern problems of mechanics, Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 281, MAIK Nauka/Interperiodica, Moscow, 2013, 98–126; Proc. Steklov Inst. Math., 281 (2013), 91–118
Citation in format AMSBIB
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\by A.~A.~Zobova, D.~V.~Treschev
\paper Ball on a~viscoelastic plane
\inbook Modern problems of mechanics
\bookinfo Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2013
\vol 281
\pages 98--126
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3467}
\crossref{https://doi.org/10.1134/S037196851302009X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3479935}
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\jour Proc. Steklov Inst. Math.
\yr 2013
\vol 281
\pages 91--118
\crossref{https://doi.org/10.1134/S0081543813040093}
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    • This publication is cited in the following 9 articles:
    1. Goryacheva I.G., Zobova A.A., “Dynamics of Deformable Contacting Bodies With Sliding, Rolling, and Spinning”, Int. J. Mech. Sci., 216 (2022), 106981  crossref  isi
    2. Zobova A.A., Goryacheva I.G., “Dynamics of a Viscoelastic Cylinder on a Viscoelastic Half-Space”, Acta Mech., 231:6 (2020), 2217–2230  crossref  mathscinet  isi
    3. Zobova A.A., “Dry Friction Distributed Over a Contact Patch Between a Rigid Body and a Visco-Elastic Plane”, Multibody Syst. Dyn., 45:2 (2019), 203–222  crossref  mathscinet  isi  scopus
    4. Goryacheva I.G., Zobova A.A., “Dynamics of the Motion of An Elastic Cylinder Along An Elastic Foundation”, Mech. Sol., 54:2 (2019), 271–277  crossref  isi  scopus
    5. O A Vinogradova, “The dynamics of a cylinder on a vibrating plane with friction”, J. Phys.: Conf. Ser., 1264:1 (2019), 012017  crossref
    6. A. V. Karapetyan, A. A. Zobova, “Tippe-top on visco-elastic plane: steady-state motions, generalized smale diagrams and overturns”, Lobachevskii J. Math., 38:6 (2017), 1007–1013  crossref  mathscinet  zmath  isi  scopus
    7. A. A. Zobova, “A review of models of distributed dry friction”, Pmm-J. Appl. Math. Mech., 80:2 (2016), 141–148  crossref  mathscinet  isi  scopus
    8. A. V. Borisov, Yu. L. Karavaev, I. S. Mamaev, N. N. Erdakova, T. B. Ivanova, V. V. Tarasov, “Eksperimentalnoe issledovanie dvizheniya tela s osesimmetrichnym osnovaniem, skolzyaschego po sherokhovatoi ploskosti”, Nelineinaya dinam., 11:3 (2015), 547–577  mathnet
    9. Alexey V. Borisov, Yury L. Karavaev, Ivan S. Mamaev, Nadezhda N. Erdakova, Tatyana B. Ivanova, Valery V. Tarasov, “Experimental Investigation of the Motion of a Body with an Axisymmetric Base Sliding on a Rough Plane”, Regul. Chaotic Dyn., 20:5 (2015), 518–541  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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