Damage identification on spatial arches

In the paper the dynamic behavior of spatial structures composed by assemblies of circular arches is studied in both undamaged and damaged states. The exact natural frequencies of vibration are evaluated by means of the Wittrick and Williams algorithm once the dynamic stiffness matrix of the entire structure is known. The analytical functions of the modes of vibration are plotted allowing to recognize either in-plane or out of plane behaviors for each arch element. The presence of damage is considered introducing a reduction in the dimension of the cross section. Depending on the extension of the zone of reduced cross section, concentrated and diffused damages can therefore be considered. Furthermore the amount of reduction of the cross section can model intense or weak damages. Therefore three damage parameters are taken into account i.e location, intensity and extension of a single damage. In the direct problem a parametric study is developed showing the effect of the damage parameters on the natural frequencies of vibration. The inverse problem, related to the identification of the above three damage parameters, is studied through the minimization of an appropriate objective function which measures the difference between the natural frequencies in the damaged and undamaged states. Reference is made to pseudo-experimental values of the natural frequencies and numerical applications are presented.