The full nonlinear crack detection problem in uniform vibrating rods

The basic problem in structural diagnostics via dynamic methods consists in determining the position and severity of a single open crack in a beam from the knowledge of a pair of resonant or antiresonant frequencies. A well-established theory is available for longitudinally vibrating uniform beams when the severity of the crack is small. In this paper we fill the gap present in the literature by showing that the results of the linearized theory for slight damage can be extended to a crack with any level of severity.