Forced vibrations of a rolling tyre

Abstract

We investigate forced vibrations of a loaded tyre rolling at constant speed without slipping in the contact area. A previously proposed analytical model of a reinforced tyre is considered. The tyre surface is represented by flexible tread, combined with elastic sidewalls. The contact between the wheel and the ground plane occurs by the part of the tread. The dynamic components of the tread tension, of the longitudinal and normal reaction components in the contact area and of the external forces and torque applied to the wheel disc during vibrations are found analytically. The mode shapes (MS) of a loaded rotating tyre are determined analytically in the case of forced vibrations with harmonic input with both the same and different driving frequencies (DF) in horizontal and vertical directions. If the DF are different, then two corresponding MS are extracted from the spectrum and are superimposed on each other. The counter-rotating wave, which is the superposition of two MS, is observed.