Vibrational response prediction of a pneumatic tyre using an orthotropic two-plate wave model

A wave model to predict the vibrational response of a pneumatic tyre subject to line force excitation is presented. The tread and sidewalls are each modelled as thin, flat orthotropic plates with in-plane tension, which are joined together by a translational stiffness, and to a rigid rim. The dynamic response of the tyre to harmonic excitation is decomposed into spatial harmonics around the circumference, and waves in the meridional direction. At low frequencies (<100 Hz), the response is stiffness-like, and is controlled by the sidewall properties and tension effects resulting from the tyre pressure. In the mid-frequency range (100–500 Hz), a resonant response is observed, associated with modes both across and around the tyre. At high frequencies (>500 Hz), the response tends towards that of an infinite orthotropic plate. Experiments have been conducted on an inflated tyre fitted to a wheel rim to confirm the theoretical findings. The results show reasonable agreement with the predictions, the model accurately reflecting the phenomenological behaviour.