Crack detection in elastic beams by static measurements

Abstract

This paper deals with the identification of a single crack in a beam based on the knowledge of the damage-induced variations in the static deflection of the beam. The crack is simulated by an equivalent linear spring connecting the two adjacent segments of the beam. Sufficient conditions on static measurements which allow for the unique identification of the crack are presented and discussed. The inverse analysis provides exact closed-form expressions of position and severity of the crack as functions of deflection measurements for different boundary conditions. The theoretical results are confirmed by a comparison with static measurements on steel beams with a crack. Extension of the presented analysis to multiple cracks is briefly discussed

Estimation of structural parameters using static loading tests

“…Nevertheless, no particular noise treatment is proposed. Caddemi & Morassi (2007) develop closed-form expressions for the determination of the location and magnitude of cracks in beams, subjected to different boundary conditions (pinned-pinned, pinned-clamped and clampedfree). Cracks are modelled as rotationary springs of constant related to the severity of the damage.…”

“…As damage can be characterized as a local reduction in structural stiffness, analysis of the structure's static response has been used extensively to locate and quantify damage (Sanayei & Scampoli, 1991;Hjelmstad & Shin, 1997;Bakhtiari-Nejad et al, 2005;Caddemi & Morassi, 2007, Walsh & Gonzalez 2009and Yang & Sun, 2010. Most of these methods use a finite element (FE) mathematical model as reference, and deflections and rotations as inputs.…”

Free Vibration Analysis of a Rotating Non-Uniform Blade with Multiple Open Cracks Using DQEM

“…For higher-order derivatives, this matrix can be obtained from a recursive relation as A (r) =A (1) A (r-1) . In addition to number of grid points, distribution of them is an important factor in convergence of solution.…”

“…Several authors have proposed techniques to estimate the effects of damage on the eigen parameters of a structure (usually known as the direct problem), while others have dealt with the problem of detecting, locating and quantifying the extent of damage (well-known as the inverse problem). A few authors have addressed aspects concerning the identification of the cracks, leading to explicit expressions for the solution of the inverse problem [1]. Also, variation of the natural frequencies with the depth and position of a concentrated crack has been explained in the references such as Morassi [2,3] and Narkis [4].…”

The Hu–Washizu variational principle for the identification of imperfections in beams

“…Moreover, the presented procedure will be shown to be suitable for identification of concentrated damages that is a subject to which a great interest has been devoted in the specific literature [3,7,8,10,11,14,15,24,25]. Recently, a model of the Euler-Bernoulli beam with singularities able to model the presence of concentrated damages has been proposed [20,[29][30][31].…”