Bridge structures are continuously subject to degradation due to the environment, ageing and excess loading. Periodic monitoring of bridges is therefore a key part of any maintenance strategy as it can give early warning if a bridge becomes unsafe. This article investigates an alternative method for the monitoring of bridge dynamic behaviour: a truck-trailer vehicle system, with accelerometers fitted to the axles of the trailer. The method aims to detect changes in the damping of a bridge, which may indicate the existence of damage. A simplified vehicle-bridge interaction model is used in theoretical simulations to assess the effectiveness of the method in detecting those changes. The influence of road profile roughness on the vehicle vibration is overcome by recording accelerations from both axles of a trailer and then analysing the spectra of the difference in the accelerations between the two axles. The effectiveness of the approach in detecting damage simulated as a loss in stiffness is also investigated. In addition, the sensitivity of the approach to the vehicle speed, road roughness class, bridge span length, changes in the equal axle properties and noise is investigated.