Vibration analysis of damaged circular arches with varying cross-section

In this paper, generalized differential quadrature techniques are applied to the computation of the in-plane free vibrations of thin and thick non-uniform circular arches in undamaged and damaged configurations, when various boundary conditions are considered. Structural damage is represented by one crack in different positions and with various damage levels. The crack present in a structural member can be considered as a local stiffness reduction at the fracturing section, which changes the dynamic behaviour of the structure. Much effort has been devoted to dealing with in-plane free vibration analysis of circular arches, but only a few researchers have studied cracked circular arch structures. The present analysis refers to the complete in-plane equations of motion of non-uniform circular arches, in terms of displacements and rotation. Shearing and axial deformations as well as rotary inertia are taken into account. For given geometric and boundary conditions, the presence of a crack will cause displacements and rotations of sections along the arch greater than the corresponding values resulting in an uncracked structure. In order to evaluate the effect of cracks, a cracked section is modelled as an elastic hinge with rotational constant which has to simulate the local flexibility caused by the cracked section itself. A crack will produce discontinuities in slope of the elastic curve of the arch at the fractured cross-section. It should be noted that in our investigation of the in-plane dynamic response variation of damaged arches with variable cross-section, the localized cracks will always be considered as open.