Vibration of locally cracked pre-loaded parabolic arches

We study linear dynamics of an initially parabolic arch deformed by a uniform 'dead' load. The arch is seen as a fully deformable one-dimensional continuum with rigid cross-sections, one of which suffers from a small local crack at its boundary. The crack is simulated by springs, the stiffnesses of which are evaluated via stress intensity factors. By two first-order perturbations we investigate a non-trivial equilibrium adjacent to the reference configuration and small vibration superposed on it. The modulation of the initial load on the natural angular frequencies and its consequences on damage detection is described and commented. It turns out that neglecting the initial load, recalling for actual 'dead' structural actions, can be misleading in damage identification, while its inclusion leads to better results.