Influence of vehicle-road coupled vibration on tire adhesion based on nonlinear foundation

The influence of pavement vibration on tire adhesion is of great significance to the structure design of vehicle and pavement. The adhesion between tire and road is the key to studying vehicle dynamics, and the precise description of tire adhesion affects the accuracy of dynamic vehicle responses. However, in most models, only road roughness is considered, and the pavement vibration caused by vehicle-road interaction is ignored. In this paper, a vehicle is simplified as a spring-mass-damper oscillator, and the vehicle-pavement system is modeled as a vehicle moving along an Euler-Bernoulli beam with finite length on a nonlinear foundation. The road roughness is considered as a sine wave, and the shear stress is ignored on the pavement. According to the contact form between tire and road, the LuGre tire model is established to calculate the tire adhesion force. The Galerkin method is used to simplify the partial differential equations of beam vibration into finite ordinary differential equations. A product-to-sum formula and a Dirac delt function are used to deal with the nonlinear term caused by the nonlinear foundation, which realizes the fast and accurate calculation of super-high dimensional nonlinear ordinary differential equations. In addition, the dynamic responses between the coupled system and the traditional uncoupled system are compared with each other. The obtained results provide an important theoretical basis for research on the influence of vehicle-road coupled vibration on tire adhesion.