Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Rolling contact between dissimilar viscoelastic cylinders


Author: L. W. Morland
Journal: Quart. Appl. Math. 25 (1968), 363-376
DOI: https://doi.org/10.1090/qam/99875
MathSciNet review: QAM99875
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Abstract | References | Additional Information

Abstract: This paper treats the plane problem of rolling contact between linear viscoelastic cylinders with different radii and different quantitative mechanical response. The analysis is an extension of that previously given for the simpler problem of rolling contact between two identical cylinders (or equivalently one cylinder and a rigid half-plane), for which a singular integral equation was derived connecting pressure and normal displacement in the contact region. The present problem is shown to lead to an integral equation of identical form but containing further parameters which reflect the difference in the properties of the two cylinders. A neater construction of the closed form solution of the integral equation is presented and the final formulae are expressed in terms of tabulated functions. An illustration is given for a viscoelastic model with two characteristic times.


References [Enhancements On Off] (What's this?)

  • [1] L. W. Morland, Exact solutions for rolling contact between linear viscoelastic cylinders, Quart. J. Mech. Appl. Math. 20, 73 (1967) MR 0210364
  • [2] F. G. Tricomi, Integral equations, Interscience, New York, 1957 MR 0094665
  • [3] G. N. Watson, A treatise on the theory of Bessel functions, 2nd ed. Cambridge Univ. Press, Oxford, 1944 MR 0010746
  • [4] S. C. Hunter, The rolling contact of a rigid cylinder with a viscoelastic half space, J. Appl. Mech. 28, 611 (1961)


Additional Information

DOI: https://doi.org/10.1090/qam/99875
Article copyright: © Copyright 1968 American Mathematical Society

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