Wave Content of the Vibration Field of a Rolling Tyre

In order to calculate tyre/road noise generated by tyre vibrations, the vibration velocity field on a rolling tyre is required. Previously a three-dimensional contact model was presented, which makes it possible to calculate the time-varying radial contact forces at the contact patch. The contact forces result from the tyre/road interaction in rolling conditions. Knowing the contact forces and the vibrational properties of the tyre structure, the vibrational velocity field can be calculated. This paper describes how to calculate the vibrational field on the tyre structure, especially in the wavenumber-frequency domain. The study of the static deformation of the tyre under rolling conditions and of the Doppler effect for a periodic excitation of the tyre gives some good understanding on the way the vibrational field is built up. Additionally, a study of the effect of the wave content on sound radiation is made and numerical results show that only a limited number of modes contribute to the total sound radiated by tyre structure vibrations, and that higher-order modes can be discarded.