Vibration of locally cracked pre-loaded parabolic arches

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