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Nelin. Dinam., 2011, Volume 7, Number 3, Pages 601–625 (Mi nd280)  

This article is cited in 5 scientific papers (total in 5 papers)

A rigid cylinder on a viscoelastic plane

Alexander S. Kuleshova, D. V. Treschevba, T. B. Ivanovacd, O. S. Naimushinac

a M. V. Lomonosov Moscow State University, Vorobevy gory, Moscow, 119899, Russia
b Steklov Mathematical Institute, Russian Academy of Sciences Gubkina st. 8, Moscow, 119991, Russia
c Udmurt State University, Universitetskaya st. 1, Izhevsk, 426034, Russia
d Institute of Computer Science, Universitetskaya st. 1, Izhevsk, 426034, Russia

Abstract: The paper considers two two-dimensional dynamical problems for an absolutely rigid cylinder interacting with a deformable flat base (the motion of an absolutely rigid disk on a base which in non-deformed condition is a straight line). The base is a sufficiently stiff viscoelastic medium that creates a normal pressure $p(x)=kY(x)+\nu\dot Y(x)$, where $x$ is a coordinate on the straight line, $Y(x)$ is a normal displacement of the point $x$, and $k$ and $v$ are elasticity and viscosity coefficients (the Kelvin–Voigt medium). We are also of the opinion that during deformation the base generates friction forces, which are subject to Coulomb's law. We consider the phenomenon of impact that arises during an arbitrary fall of the disk onto the straight line and investigate the disk's motion “along the straight line” including the stages of sliding and rolling.

Keywords: Kelvin–Voight medium, impact, viscoelasticity, friction

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Document Type: Article
UDC: 539.3
MSC: 70F40, 70F35, 70E18
Received: 10.05.2011
Revised: 19.08.2011

Citation: Alexander S. Kuleshov, D. V. Treschev, T. B. Ivanova, O. S. Naimushina, “A rigid cylinder on a viscoelastic plane”, Nelin. Dinam., 7:3 (2011), 601–625

Citation in format AMSBIB
\Bibitem{KulTreIva11}
\by Alexander~S.~Kuleshov, D.~V.~Treschev, T.~B.~Ivanova, O.~S.~Naimushina
\paper A rigid cylinder on a viscoelastic plane
\jour Nelin. Dinam.
\yr 2011
\vol 7
\issue 3
\pages 601--625
\mathnet{http://mi.mathnet.ru/nd280}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Zobova, D. V. Treschev, “Ball on a viscoelastic plane”, Proc. Steklov Inst. Math., 281 (2013), 91–118  mathnet  crossref  crossref  mathscinet  isi  elib
    2. I. S. Mamaev, T. B. Ivanova, “Dinamika tverdogo tela, opirayuschegosya ostrym kraem na naklonnuyu ploskost, pri nalichii sukhogo treniya”, Nelineinaya dinam., 9:3 (2013), 567–593  mathnet
    3. I. S. Mamaev, T. B. Ivanova, “The dynamics of a rigid body with a sharp edge in contact with an inclined surface in the presence of dry friction”, Regul. Chaotic Dyn., 19:1 (2014), 116–139  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. E. N. Pivovarova, A. V. Klekovkin, “Vliyanie treniya kacheniya na upravlyaemoe dvizhenie robota-kolesa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:4 (2015), 583–592  mathnet  elib
    5. A. A. Zobova, “A review of models of distributed dry friction”, J. Appl. Math. Mech., 80:2 (2016), 141–148  crossref  isi
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