This paper analyzes the interaction between a heavy vehicle and a simply supported light bridge based on frequency modulation technique, in which variations of instantaneous frequencies of both bridge and heavy vehicle are considered. The bridge is modeled as a simply supported Euler beam and the heavy vehicle is simplified as a spring-mass system. The variation of instantaneous frequencies of both bridge and vehicle induced by the moving vehicle is usually neglected in classical analysis to decouple the pair of governing equations. However, the coupled vehicle–bridge interaction (VBI) system becomes time-varying and the pair of governing equations cannot be decoupled when the vehicle/bridge mass ratio cannot be neglected. The instantaneous frequencies of both bridge and heavy vehicle including their higher vibration modes are investigated herein. An analytical solution describing the dynamic response of the time-varying VBI system is developed by using the frequency modulation technique. Both Finite Element (FE) method and published experimental data are used for comparison purpose. The predictions of the proposed method match better with those obtained from the FE simulations and experimental measurements than the classical method. Five numerical examples have been adopted to compare the performance of the proposed model and the classical method: the former performs generally well, especially when the vehicle is heavy, or the vehicle frequency is near to the bridge frequency. The classical method is only a special case of the proposed model if either the mass or the stiffness of the vehicle is relatively small compared to the corresponding terms of the bridge. The performance of the proposed method has also been examined in four typical scenarios, where vehicle damping, multi-degree-of-freedom (MDOF) vehicle, road surface roughness, and two-span continuous bridge are involved.

中文翻译：

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基于频率调制的重型车辆与简支轻型桥梁相互作用的解析分析

本文基于频率调制技术分析了重型车辆与简支轻型桥梁的相互作用，其中考虑了桥梁和重型车辆瞬时频率的变化。桥梁被建模为简单支撑的欧拉梁，重型车辆被简化为弹簧质量系统。经典分析中通常忽略由移动车辆引起的桥梁和车辆瞬时频率的变化，以解耦这对控制方程。然而，耦合的车桥相互作用（VBI）系统成为时变的，当不能忽略车桥质量比时，这对控制方程不能解耦。本文研究了桥梁和重型车辆的瞬时频率，包括它们的较高振动模式。通过使用频率调制技术，开发了描述时变 VBI 系统动态响应的解析解。有限元 (FE) 方法和公布的实验数据均用于比较目的。与经典方法相比，所提出方法的预测与从有限元模拟和实验测量中获得的预测更好地匹配。采用五个数值例子比较了所提出模型和经典方法的性能：前者表现一般，特别是当车辆较重或车辆频率接近桥频时。如果车辆的质量或刚度与桥梁的相应项相比相对较小，则经典方法只是所提出模型的一种特殊情况。