Abstract
Despite the numerous explicit solutions of free vibration of arches with regular cross sections, in case of concentrated defects such as cracks, no procedure is available to analyse arch vibrations without sub-division of the integration domain. As a result, curved sub-elements comprised between crack and external constraints, or successive cracks, are considered.In this paper a distributional approach is adopted to provide a formulation of the free vibration differential governing equations of circular inextensible arches over a unique integration domain in presence of multiple concentrated open (non-breathing) cracks. Discontinuities due to the presence of an arbitrary number of cracks are modelled by means of Dirac's deltas. An integration procedure is devised to offer closed form solutions of the relevant vibration modes together with the relevant frequency determinantal equation. Natural frequencies and mode shapes of damaged arches with different damage and restraint configurations have been evaluated and compared with experimental results available in the literature as well as finite element numerical simulations. The presented closed form solutions are also employed for two parametric studies to evaluate the influence of an increasing number of along axis concentrated cracks as well as of the location of cracks along the arch span.
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