Analysis for tire dynamic response rolling over an obstacle is important to study automobile NVH (Noise‐Vibration‐Harshness), determine vehicle fatigue load, investigate combined longitudinal and sideslip properties, and develop ABS system on uneven roads. Based on the model of Ring on the Elastic and Viscoelastic Foundation (REF) and its analytical solution previously developed, the rolling contact problem between tire/flat and tire/cleat is dealt with in this paper. The static contact problem is treated as the first step to show the effectiveness and accuracy of the model. Then, the time domain simulation of tire rolling contact on uneven roads is conducted. Meirovitch modal analysis method and first‐order matrix perturbation theory are applied to obtain the general forced response of damping REF vibration. An effective numerical quadrature method is developed to obtain the time‐varying modal coordinates of the system under various loading conditions. Numerical examples of a tire rolling over a cleat are given to verify the developed method. It is found that both damping and velocity have strong effects on tire response over a cleat and the frequency of dynamic load is mainly controlled by the first tire mode.

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