A wave model of a circular tyre. Part 1: belt modelling

The equations of motion of a curved tyre belt are derived for one-dimensional waves propagating around the belt and a standing wave across the belt. The effects of curvature, shear stiffness, rotary inertia, tension, rotational speed and air pressure are included. These are combined to give a sixth-order wave equation, the solution of which gives three pairs of wavenumber as a function of frequency. The application of the boundary conditions at the contact leads to the input and transfer mobilities for both in-plane and out of plane excitation. Observed are: low-frequency rigid-body modes, belt bending modes and in-plane ring modes. At high frequencies only travelling waves occur.