Localisation and quantification of stiffness loss based on the forced vibration of a beam traversed by a quarter-car

This paper proposes a method for locating and quantifying bridge damage based on the time-varying forced frequencies due to moving traffic. The vehicle-bridge coupled system is simplified using a quarter-car model and a simply supported beam. Eigenvalue analysis shows that the eigenfrequencies of the coupled system vary for different vehicle positions. If a local stiffness loss is introduced, the forced frequencies associated with the ‘damage’ scenario will differ from those of a reference ‘healthy’ scenario. The differences between both scenarios depend on the location and severity of damage as well as on the mass and frequency ratios between quarter-car and beam models. In practice, bridge acceleration due to the crossing of a vehicle can be measured and processed using a time-frequency signal processing tool to obtain instantaneous frequencies. Changes in local stiffness are determined from comparing those instantaneous frequencies with the eigenfrequencies based on the same bridge and vehicle configuration.