Self-oscillations during car braking / V. G. Vil'ke, I. L. Shapovalov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 4. P. 33-39 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 0].
Motion of the automobile after blocking wheels whose sliding on a road is described by a model of nonlinear viscous friction with a falling segment of the characteristic is considered. The used model of friction approximates a model of dry friction when the friction of rest surpasses the sliding friction. In this case, the self-oscillations of wheels are observed at some stages of braking of the automobile under the appropriate initial conditions of motion. These self-oscillations generate a periodically varied tangential loading on a roadbed, which may cause the appearance of a wavy relief on the road. Such a wavy relief is most often observed on soil roads at the turns during the intensive braking process. The study of the character of motion is illustrated by numerical examples for the Lagrange equations of the second kind and for the equations derived by a method of averaging the canonical equations written in the action–angle variables.
Key words: model of the automobile with a suspension bracket, model of nonlinear viscous friction, self-oscillation during braking the automobile.