UC Berkeley

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.