The vibrations of a free and loaded tyre

Using the model of a wheel with a reinforced tyre [Vil’ke VG, Kozhevnikov IF. A model of a wheel with a reinforced tyre. Vestnik MGU. Ser.1. Matematika Mekhanika 2004;4:37–45], the natural frequencies and natural forms of vibrations of a free or loaded tyre in the neighbourhood of the equilibrium position are determined. The spectrum of natural frequencies and natural forms of vibration are found analytically for a free (unloaded) tyre with a fixed disc. A similar problem is solved numerically in the case of a loaded tyre. The results of this analysis can be used to estimate the level of noise which occurs when a vehicle moves on an uneven surface.