Detection of localised damage in plane circular arches by frequency data

The possibility to detect the structural damage affecting a narrow zone of a doubly hinged plane circular arch by means of a few measured natural frequencies is considered. Such localised damage induces a discontinuity in the bending stiffness of the arch, modelled as a torsion spring joining two adjacent sections and characterised by the location and the stiffness of the spring. The direct problem in the damaged and undamaged case is examined; the inverse problem is then considered. Two different procedures to identify the damage parameters are introduced: the first is based on the search of an intersection point of curves obtained by the modal equation; the second is based on the comparison between the analytical and experimental values of the variation of frequencies passing from the undamaged to the damaged state. In conclusion, the possibility of identifying the damage parameters by means of pseudo-experimental data is examined.