Consideration of the problem about vibration of automobile in one fourth model with taking road deformation and the loss of contact into account

This paper presents an approach to the problem about vibration of automobiles in one-fourth model where both road deformation and the loss of contact are taken into account. Contact characteristics such as the geometry of the contact area, pressure distribution, the relation between the contact force and the dimensions of the contact area, and therefore the change in dimensions of the contact area with respect to time are mentioned. Deformed road is modeled as an elastic beam which is simply supported at the two ends and lies on Kelvin’s visco-elastic ground. The differential equations of motion for both states of contact and losing contact are unified by introducing a so-called contact state parameter. The partial differential equation among the differential equations of motion of the vehicle-road coupled system is transformed into a system of all ordinary differential equations by applying the Bubnov-Galerkin’s method. A procedure for numerically solving the ordinary differential equations of motion of the vibration system under consideration is proposed and some numerical results for illustration are also presented in the paper. © 2020 Ham Vu Cong, et al.