Theoretical vehicle bridge interaction model for bridges with non-simply supported boundary conditions

Abstract

Theoretical vehicle bridge interaction (VBI) models have been widely studied for decades for the simply supported boundary condition but not for the other boundary conditions. This paper presents the mathematical models for several non-simply supported boundary conditions including both ends fixed, fixed simply supported, and one end fixed the other end free (cantilever) boundary condition. The closed-form solutions can be found under the assumption that the vehicle acceleration magnitude is far lower than the gravitational acceleration constant. The analytical solutions are then illustrated on a specific bridge example to compare the responses due to different bridge boundary conditions, and to study different vehicle parameter effects on extracting multiple bridge frequencies (five) from the vehicle responses. A signal drift phenomenon can be observed on the acceleration response of both the bridge and the vehicle, while a camel hump phenomenon can be observed on the Fast Fourier analysis of the vehicle acceleration signal. The parameter study shows that the vehicle frequency is preferred to be high due to the attenuation effect on the bridge frequencies that are higher than the vehicle frequency. The vehicle speed parameter is preferred to be low to reduce both the camel hump phenomenon and the vehicle acceleration magnitude, while both the vehicle mass and damping parameter have little effect on the multiple bridge frequencies extraction from the vehicle. Besides presenting the explicit solutions for calibrating other numerical models, this study also demonstrates the feasibility of the vehicle-based bridge health monitoring approach, as any bridge anomaly due to deterioration may be sensitively reflected on the bridge frequency list extracted from the vehicle response.