Analytical Analysis of Interaction Between a Heavy Vehicle and a Simply Supported Light Bridge Based on Frequency Modulation

Abstract

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.