Cao, R. and Bolton, J., "Improved Model for Coupled Structural-Acoustic Modes of Tires," SAE Int. J. Passeng. Cars - Mech. Syst. 8(3):845-854, 2015, doi:10.4271/2015-01-2199.
Experimental measurements of tire tread band vibration have provided direct evidence that higher order structural-acoustic modes exist in tires, not just the well-known fundamental acoustical mode. These modes display both circumferential and radial pressure variations within the tire's air cavity. The theory governing these modes has thus been investigated. A brief recapitulation of the previously-presented coupled structural-acoustical model based on a tensioned string approach will be given, and then an improved tire-acoustical model with a ring-like shape will be introduced. In the latter model, the effects of flexural and circumferential stiffness are considered. This improved model accounts for propagating in-plane vibration in addition to the essentially structure-borne flexural wave and the essentially airborne longitudinal wave accounted for in the previous model. The longitudinal structure-borne wave “cuts on” at the tire's circumferential ring frequency. Explicit solutions for the structural and acoustical modes will be given in the form of dispersion relations. The latter results will be compared with measured dispersion relations, and the features associated primarily with the higher order acoustic modes will be highlighted. Finally, the effect of tire rotational speed on the natural frequencies of these various modes types will also be discussed.