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.

[1]  Y.B. Yang,et al.  Damage detection of plate-type bridges using uniform translational response generated by single-axle moving vehicle , 2022, Engineering Structures.

[2]  Philippe B. Laval,et al.  The laplace transform , 1991, Heat Transfer 1.

[3]  G. Manolis,et al.  Model Bridge Span Traversed by a Heavy Mass: Analysis and Experimental Verification , 2021, Infrastructures.

[4]  Mijia Yang,et al.  Possibility of Bridge Inspection through Drive-By Vehicles , 2020, Applied Sciences.

[5]  Wei-Xin Ren,et al.  Damage localization of beam structures using mode shape extracted from moving vehicle response , 2018, Measurement.

[6]  D. Chalishajar,et al.  On Applications of Generalized Functions in the Discontinuous Beam Bending Differential Equations , 2016 .

[7]  Mijia Yang,et al.  Dynamic responses of prestressed bridge and vehicle through bridge–vehicle interaction analysis , 2015 .

[8]  Eugene J. O'Brien,et al.  Identification of bridge mode shapes using Short Time Frequency Domain Decomposition of the responses measured in a passing vehicle , 2014 .

[9]  Raid Karoumi,et al.  Analysis of the annual variations in the dynamic behavior of a ballasted railway bridge using Hilbert transform , 2014 .

[10]  Kay Smarsly,et al.  A migration-based approach towards resource-efficient wireless structural health monitoring , 2013, Adv. Eng. Informatics.

[11]  Andrzej Katunin,et al.  Crack identification in composite elements with non-linear geometry using spatial wavelet transform , 2013 .

[12]  Arturo González,et al.  An Investigation into the Acceleration Response of a Damaged Beam-Type Structure to a Moving Force , 2013 .

[13]  Pizhong Qiao,et al.  Vibration of beams with arbitrary discontinuities and boundary conditions , 2007 .

[14]  T. Chondros,et al.  VIBRATION OF A BEAM WITH A BREATHING CRACK , 2001 .

[15]  Andrew D. Dimarogonas,et al.  Vibration of cracked structures: A state of the art review , 1996 .

[16]  T. Chondros,et al.  Dynamics of Cracked Shafts , 2013 .

[17]  Viorel Barbu,et al.  Distributed Parameter Systems , 1992, Concise Encyclopedia of Modelling & Simulation.