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1.1 MATHMATICS, 1.2 COMPUTER AND INFORMATION SCIENCE
The problem of a viscoelastic cylinder rolling on a rigid base, propelled by a line force acting at its centre, is solved in the noninertial approximation. The method used is based on a decomposition of hereditary integrals developed by the authors in previous work, and on the viscoelastic Kolosov-Muskhelishvili equations which are used to generate a Hilbert problem. In this formulation, the problem reduces to a nonsingular integral equation in space and time, which simplifies under steady-state conditions and for exponential decay materials, to algebraic form. There are also two subsidiary conditions.
In the case of a standard linear model, explicit analytic results and numerical examples are given for the pressure function, for surface displacements, and also for hysteretic friction.
Golden, J.M. & Graham, G.A.C. (2001). The Problem of a Viscoelastic Cylinder Rolling on a Rigid Half-Space. Mathematical and Computer Modelling, vol. 34, no. 12-13, pg. 1363-1397. 10.1016/S0895-7177(01)00136-4