On the Detection of Fracture within Vibrating Beams Traversed by a Moving Force

In this work, we examine the influence of a crack in the span of a beam as it is being traversed by a point force with constant velocity. This problem presents two types of discontinuities: one spatial, where the crack is modelled as a discontinuity in the slope of the deflection curve of the beam, and a temporal one, with the former derived as the point force moves forward in time. The aim is to interpret time signals registered at a given node on the beam, either during the forced vibration or the free vibration regimes, by using the Gabor transform of the transient beam response so as to observe a pattern that alludes to the location of the discontinuity. Three analytical methods are examined, namely eigenvalue extraction, Laplace transformation and the transform matrix technique. A numerical example is presented using the Laplace transformation, where it is possible to detect the location of damage during the traverse of a point force across the bridge span. Validation studies of the methodology presented here can be conducted in the future, either through field measurements or through experimental setups, which constitutes an important step in realizing applications in structural health monitoring of civil engineering infrastructure.