On the rolling of a monowheel on a deformable beam lying on two supports

A method for calculating the main mode of vibrations of an elastic-viscous beam lying on two elastic supports of different heights when a monowheel moves along it with a constant longitudinal velocity is presented. The equations of motion of the monowheel corresponding to the main mode of oscillations of the system are obtained. A method for calculating the average vibration frequency of a monowheel on a beam is proposed. An approximate averaged solution has been found that allows us to analytically assess the influence of system parameters on its dynamics. The results of numerical experiments to estimate the accuracy of the approximate solution are presented.