Green's functions for a rotating tyre: a semi-analytical approach

Road traffic noise is becoming an increasingly big problem in densely populated areas. One of the main contributions comes from the tyre/road interaction. For the interior noise, to which the occupants of the vehicle are exposed, tyre/road noise is also an important source, especially at lower frequencies. The vibrations of the tyre up to 500 Hz are transmitted via structural transmission paths to the interior effectively, thus causing acoustic noise. In this frequency range tyre/road noise is dominated by vibrational mechanisms. One of the aspects that has to be taken into account when modelling tyre vibrations is the effect of rotation. Recently a Finite Element (FE) based methodology has been presented for the modeling of rotating tyres at frequencies up to 500 Hz. A modal approach is used to determine the response of a rotating tyre. In order to solve the contact problem the unit impulse response functions (Green’s functions) of the tyre including rotation are needed. In the present paper an analytical expression of the Green’s functions including rotation based on this methodology is derived. It is shown that the frequency shift due to rotation is correctly predicted by the derived Green’s functions