Crack identification in rods and beams under uncertain boundary conditions

Abstract

This paper deals with the inverse problem of identifying a crack in a rod in axial vibration with partially unknown end conditions from a minimum number of resonant frequency variations. It is assumed that the crack is small and is modelled by an elastic spring acting along the rod axis. A first set of results concerns a uniform bar with both ends restrained by means of elastic springs having unknown flexibility. Under the hypothesis that the flexibility caused by the crack is small and of the same order of the flexibility of the elastic end constraints, it is shown that the inverse problem can be formulated in terms of the variations of the first three natural frequencies measured from the undamaged bar under ideal condition of fixed ends. It is proved that knowledge of this set of eigenfrequency variations can uniquely determine the overall flexibility induced by the end conditions, and the position (up to symmetry) and severity of the crack, by means of closed form expressions. The identification method can be also applied to axial vibrations of uniform cantilevers with elastically restrained end condition, and to transversely vibrating uniform beams either under elastic transverse support at both ends or under cantilever end conditions. The method was verified by numerical simulation and, in the case of the cantilever in bending vibration, by experimental data. Numerical analysis allowed to study in detail some singular situations occurring in the mathematical formulation of the inverse problem and to test the robustness of the method to errors on the data.

Natural frequencies of parabolic arches with a single crack on opposite cross-section sides

“…Many other contributions focus on damage identification, for instance by evaluating structural static response; this is done in Morassi (2007, 2011), Greco and Pau (2011), Greco et al (2018b), just to quote a few relatively recent examples. Very promising, damage identification techniques still debated among researchers, rely on the analysis of dynamic response; relatively recent instances of contributions in this field are those by Eroglu and Tufekci (2016), Dilena et al (2017), andFernandez-Saez et al (2017).…”

Predicting crack through a well generalized and optimal tree-based regressor

“…Their survey report is mainly based on image processing in which they have stated the challenges and the achievement in the area of crack detection. Dilena et al (2017) have explained their research work on crack detection in rods and beam like structures to identify the crack with minimum number of resonant frequencies. Crack is modeled like an elastic spring with unknown flexibility.…”