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Dynamics and Stability of Rolling Viscoelastic Tires

  • Author(s): Potter, Trevor;
  • Advisor(s): Wilkening, Jon;
  • et al.

Current steady state rolling tire calculations often do not include

treads because treads destroy the rotational symmetry of the tire.

We describe two methodologies to compute time periodic

solutions of a two-dimensional viscoelastic tire with treads:

solving a minimization problem and solving a system of equations.

We also expand on work by Oden and Lin on free spinning rolling elastic tires

in which they disovered a hierachy of $N$-peak steady state standing wave solutions.

In addition to discovering a two-dimensional hierarchy of standing wave solutions that

includes their $N$-peak hiearchy,

we consider the effects of viscoelasticity on the standing wave solutions.

Finally, a commonplace model of viscoelasticity used in our numerical experiments

led to non-physical elastic energy growth for large tire speeds.

We show that a viscoelastic model of Govindjee and Reese remedies the problem.

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