Based on the classical ring on foundation model for the tire, the effect which structural damping has on the development of the standing wave phenomenon is investigated. In particular, the model employed consists of a rotating ring on foundation where, in addition to including Coriolis effects, Kelvin-Voigt-type viscoelasticity is admitted in both the ring and foundation. Enforcing strict periodicity in space and time, the exact solution is obtained to the stated problem. Several parametric numerical experiments employing this solution are reported. These demonstrate that the standing wave phenomenon in tires is essentially a viscoelastic-type resonance response.