In this study, a low degree-of-freedom mechanical model of a rolling tire is constructed, in which the lateral deformation of the contact patch and tire carcass is considered. The so-called delayed contact patch model is implemented and combined with a simple tire carcass model. The interaction between the contact patch and the carcass together with the lateral mode of the attached suspension system is modeled by means of minimum number of relevant parameters in a simplified way in order to construct analytical results. Critical parameter ranges of self-excited vibrations are determined against the longitudinal speed of the tire. The intricate shapes of the corresponding tire deformations are presented by means of numerical simulations.

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