Vibration of locally cracked pre-loaded parabolic arches

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