Vibration characteristics of vehicle-pavement coupled system with non-uniform dynamic tire model based on nonlinear Timoshenko foundation beam

To thoroughly examine the complex relationships between tire and pavement vibrations, a sophisticated vehicle-pavement coupled system is proposed, incorporating a non-uniform dynamic friction force between the tire and the pavement. According to the Timoshenko beam theory, a dynamic model of pavement structure with a finite length beam was formulated on a nonlinear Pasternak foundation. To more accurately describe the coupling relationship between the tire and the pavement, and to take into account the vibration state under vehicle-pavement interaction, the load distribution between the tire and the pavement is modeled as a dynamic non-uniform contact. Combined with the classic LuGre tire model, the adhesion between the tire and the pavement is calculated. The Galerkin truncation method is employed to transform the pavement vibration partial differential equation into a finite ordinary differential equation, and the integral expression of the nonlinear foundation beam term is derived using the product to sum formula. By using the Runge-Kutta method, the tire-road coupled system can be numerically calculated, thus determining tire adhesion. This research demonstrates that compared with tire force under the traditional static load distribution, load distribution has a significant influence on adhesion. This study offers valuable insights for pavement structure design and vehicle performance control.