Abstract Summary
In the last decades, an increasing number of researchers has been devoted to damage detection in civil structures. Structural Health Monitoring techniques allow to monitor structures, localizing and in some cases, quantifying damages to prevent failures. Since a damaged structure is characterized by a change in the dynamic properties and given the global nature of the vibration based methods, in the present work a vibration based method for damage detection in beam structures is presented. The proposed technique exploits the modal characteristics of the structure to detect damages, evaluating variations in the dynamic flexibility matrix between the healthy and the damaged state. The advantage of this approach stems from the possibility to use only the lowest eigenfrequencies and mode shapes, that can be easily derived from the dynamic monitoring of the structure. Though in real case scenarios, structures can be instrumented only with a limited number of accelerometers, the developed damage localization and quantification technique can be successfully applied also when a restricted number of mode shape components is known. To this aim, a two step procedure based on the expansion of the reduced number of modal components to compute the structure flexibility matrix is proposed. In the first step, the known modal components φ^k of the damaged structure are completed using an iterative modal expansion technique, which utilizes the stiffness matrix of the structure. In the expansion procedure, only a subset of known modal components φ^s, with s < k, is used, while the remaining ones are used as control components (φ^c). Note that the stiffness matrix of the damaged structure is unknown. Hence, the subset φ^s of modal components using n × m different stiffness matrices is expanded, by considering damage in n possible locations, being the beam divided in n finite elements, with m damage intensities. By doing so, a dataset of n × m expanded modes is generated, where the set φ_(n,m)^e corresponds to the expanded modes related to the damage scenario (n, m). Note that every set of modes φ_(n,m)^e includes the control components φ_(n,m)^c. Thus, to identify the damage location and extent, the total modal assurance criterion (TMAC) between φ_(n,m)^c and φ^c is calculated. The damage scenario ( n*,m*), which provides the largest TMAC is selected for the following step. In the second step, this identification is verified using a flexibility based index. If the n* beam element indicated by the index corresponds to the one identified in the first step, the damage location and extent are determined. If this does not occur, the algorithm iterates the procedure until the two step check is verified. The proposed procedure is experimentally validated on a reinforced concrete free free beam with laboratory tests in which the structure is progressively damaged.
