Sensitivity to Damage of the Forced Frequencies of a Simply Supported Beam Subjected to a Moving Quarter-Car

The vibration of bridges under operational conditions can be measured via accelerometers to extract their dynamic features. These features can then be monitored in time, although only a reduced number of cause-effect scenarios can be verified on the field. Therefore, theoretical models of the bridge are often employed for covering a wider range of scenarios. For instance, a variety of damage conditions can be introduced in a calibrated bridge model to obtain the associated frequencies, which can be subsequently compared to frequencies measured on-site for assessing the bridge condition. It must be noted that these frequencies may be influenced by factors other than damage, i.e., environmental effects due to temperature changes and operational effects due to traffic. During the forced vibration of a bridge caused by a moving vehicle, the frequencies governing the bridge response depend on the mass and stiffness ratios of the vehicle to the bridge. Therefore, records in free vibration are usually preferred or alternatively, the influence of operational loads is removed from forced vibration records before assessing whether damage has occurred or not. This paper shows that forced vibration stores relevant information about damage beyond the frequency changes derived from free vibration. Eigenvalue analysis is employed to investigate how forced frequencies change with the positions of a crossing vehicle and damage. The vehicle is modelled using a quarter-car and the bridge as a simply supported finite element beam, where damage is introduced via localized stiffness losses.