On the theory of standing waves in tyres at high vehicle speeds

When a vehicle moves at high speed and if the speed exceeds a certain ‘critical velocity’, then quite intensive flexural waves travelling around the circumference of the tyre emerge from the trailing edge of the contact patch. To the observer these waves in the tyre appear to be stationary. Therefore, in the literature they are often referred to as ‘standing waves in tyres’. Although this phenomenon has been studied since the 1950s and a number of successful predictions of experimentally observed features had been made, it is still not well understood. In the present paper, a new physically explicit theory of tyre standing waves has been developed. The theory is based on a tensioned beam model of a tyre. Simple analytical expressions have been derived for the amplitudes and shapes of generated waves and for the most important parameter characterising the phenomenon of tyre standing waves—the vehicle critical speed beyond which the standing waves occur. The performance of the theory is examined by varying the tyre parameters and by comparing the results, where possible, to other similar work. The obtained predictions show that the developed theory explains and predicts the phenomenon of tyre standing waves surprisingly well, given its simplicity and the uncertainty in the tyre parameters used in calculations. It also has the potential for further development.