Dynamic response of a damaged bridge model traversed by a heavy point mass

Abstract

The dynamic response of a single-span, damaged bridge model traversed by a point mass whose magnitude is comparable to that of the underlying girder is studied for the purpose of detecting structural damage. Damage is represented in the form of vertical cracks running across the girder's web, which modifies the eigenproperties of the original intact girder. The weight of the mass during its traverse time also modifies the eigenproperties of the girder and its motion produces an additional damping effect. Both features are modelled as Dirac delta distributions, one accounting for the spatial discontinuity in the slope of the deflection, and the other for the temporal discontinuity as the point mass moves forward with constant velocity. Although each type of discontinuity has been treated in the past, their combined effect has not been satisfactorily addressed. Next, a novel time-marching scheme is introduced for treating the temporal discontinuity, where the mass, stiffness and damping of the girder are all updated at the end of a given time interval. Then, the equations of motion are cast as a first-order, matrix differential equation. A parametric study has shown that two eigenvalue-eigenfunction pairs are sufficient for convergence purposes. Following modal synthesis, the transient velocities at any point on the girder during both forced and free vibration regimes are processed by the short-time Fourier transform as a means for detecting changes in the resulting spectograms that are attributable to damage. Finally, support failure is also examined by the introduction of flexible translational springs at the ends. The methodology developed here can be used to identify damage from the recorded kinematic spectrograms at any station on the span of the girder due to a travelling mass. In closing, this work finds applications in structural health monitoring of structures, which is a contemporary and challenging problem facing the engineering profession.