A waveguide finite element aided analysis of the wave field on a stationary tyre, not in contact with the ground

Although tyre/road noise has been a research subject for more than three decades, there is still no consensus in the literature as to which waves on a tyre are mainly responsible for the radiation of sound during rolling. Even the free vibrational behaviour of a stationary (non-rotating) tyre, not in contact with the ground, is still not well understood in the mid- and high-frequency ranges. Thus, gaining an improved understanding of this behaviour is a natural first step towards illuminating the question of which waves on a rolling tyre contribute to sound radiation. This is the topic of the present paper, in which a model based on the waveguide finite element method (WFEM) is used to study free wave propagation, on a stationary tyre, in the range 0–1500 Hz. In the low-frequency region (0–300 Hz), wave propagation is found to be rather straightforward, with two main wave-types present. Both have cross-section modes involving a nearly rigid motion of the belt. For higher frequencies (300–1500 Hz) the behaviour is more complex, including phenomena such as ‘curve veering’ and waves for which the phase speed and group speed have opposite signs. Wave-types identified in this region include (i) waves involving mainly sidewall deformation, (ii) belt bending waves, (iii) a wave with significant extensional deformation of the central belt region and (iv) a wave with a ‘breathing’ cross-section mode. The phase speed corresponding to found waves is computed and their radiation efficiency is discussed, assuming free-field conditions. In a future publication, the tyre model will be used in conjunction with a contact model and a radiation model to investigate the contribution of these waves to radiated sound during rolling.