Dynamic analysis of a tire using a nonlinear Timoshenko ring model

It is well known that tires play an important role in the generation of rolling noise. For low frequencies, the circular ring model can describe in a simple way the tire dynamic behaviour. This model is based on the Euler Bernoulli beam theory and takes into account the prestress generated by the internal air pressure but is otherwise linear. However, nonlinear effects resulting from high internal pressure and vehicle load can be important. In particular, vehicle load generates contact forces and a non-circular geometry in stationary rolling conditions.This paper presents a nonlinear flexible ring model based on the Timoshenko beam theory. It is used to simulate the nonlinear static deformation of a tire resulting from the application of vehicle load and inflation pressure. It is also applied to study the effect of these two parameters on the dynamic behaviour of the tire around its nonlinear static state by computing normal modes and transfer functions. In both static and dynamic cases, the results are in good agreement with Abaqus simulations considered as reference.