基于无限长梁模型的车路振动耦合系统半解析解

针对无限长道路与车辆耦合系统响应计算复杂难题，考虑地基的弹性特性与道路不平度，建立基于无限长欧拉-伯努利梁模型的车路振动耦合系统。进而以车辆为参考点建立移动坐标系，提出通过积分变换推导耦合系统振动响应解析解的方法，并应用留数定理对其进行数值计算，获得车辆垂向位移、加速度、路面振动响应等系统响应的半解析解。与传统应用模态叠加法的有限长道路与车辆耦合响应相比，具有更高的计算效率与精度，系统参数化研究也证明了该半解析解的有效性。

Semi-Analytical Solution for Vehicle-Road Vibrational Coupling System Based on an Infinite-Length Beam Model

To solve the complex challenge of response calculation for the coupling system between the infinite-length road and vehicle, the elastic characteristics of foundation and road roughness are considered in the analysis, and a vehicle-road vibration coupling system is established based on an infinite length Euler Bernoulli beam model. Then, the moving coordinate system was set up using the vehicle as the reference point. The analytical solution of vibration response of the coupled system was derived by integral transformation. The numerical calculations were carried out by applying the residue theorem, and the semi analytical solutions for the vehicle''s vertical displacement, acceleration and road vibration response were obtained. Compared to the traditional modal superposition method used for the coupling response of finite-length roads and vehicles, this method achieves higher computational efficiency and accuracy. The parametric study of the system also proves the validity of the semi-analytical solution. These results provide important theoretical guidance for improving vehicle comfort as well as optimizing and controlling road friendliness.