Structural damage identification using transfer matrix with lumped crack properties

A novel damage detection scheme is developed for detecting multiple cracks in beams, based on a transfer matrix (TM) approach. Lumped Crack TM of a beam element with multiple cracks is derived based on lumped crack properties. A cracked beam element is assumed as two intact beam elements connected with a hinge or torsional spring. The crack is modelled as an element of zero length and mass, but with elastic properties. Lumped crack approach is simpler for multiple cracks than the possible alternative methods. The state vector at a node includes displacements, forces and moments at that node; when it is multiplied with TM the state vector at the adjacent node can be obtained. The crack identification strategy used here, involves measuring the initial state vector at a node, in the zone of interest. The displacements at the adjacent nodes are measured and these are predicted using TM. Using an optimization algorithm the unknown crack parameters in the TM are solved by minimizing the deviation between measured and predicted displacements. The method is verified using several numerical models as well as experiments with cracked beams. The TM is shown to be suitable for local identification and also fast and accurate compare to other methods.