Numerical and experimental detection of concentrated damage in a parabolic arch by measured frequency variations

Abstract

The dynamics of a parabolic arch is studied in its undamaged and damaged states. The damage consists of a notch that reduces the height of the cross section at a given abscissa. A damage identification technique, based on the minimization of an objective function measuring the differences between numerical and experimental variations of natural frequencies for undamaged and damaged states, is used. The uniqueness of the solution in different damage configurations is investigated using pseudo-experimental data and the reliability of the identification procedure is assessed. The identification procedure is then applied to an experimental case, where frequencies are obtained by impulsive tests on a prototype arch. The minimum number of experimental data needed to identify damage parameters is defined and the sensitivity of the identification algorithm to different possible choices of sets of data is analyzed

Dynamic Characterization and Damage Identification

“…This is shown in Figure 15, which shows the objective functions obtained when using three frequencies and wether the reduction in the axial stiffness induced by damage is considered (bold line) or not. More details can be found in (Pau et al, 2010).…”

“…It is important to distinguish between two different situations: (a) diffused damage as a consequence of an infrequent event (strong wind, earthquake, explosion, etc. ): this case is similar, but more complex than the initial identification of the structure, where it is reasonable to consider some regularity in the distribution of the mechanical characteristics, and the inverse problem exhibits a high number of unknowns, frequently leading to an indeterminate problem (Teughels and De Roeck, 2004;Morassi, 2007;Cruz and Salgado, 2008); (b) concentrated damage related to a local phenomenon of deterioration or overstress (corrosion, crack), in this case damage is located in a few sections and modifies few stiffness characteristics, which constitute a small number of unknowns, frequently leading to an over-determined problem (Vestroni and Capecchi, 1996;Capecchi and Vestroni, 2000;Pau et al, 2010).…”

A State of the Art Review of Modal-Based Damage Detection in Bridges: Development, Challenges, and Solutions

“…Generally, an assumption of linear-stationary structural response is made to allow the use of a Fourier-type transform to obtain the frequency content of measured vibration data, prior to employing peak-peaking to discern modal frequencies. The global nature of modal frequencies may not always lend itself well to damage localisation in complex structures [34][35][36], although they can be utilised to do so for more regular geometries when given the undamaged and damaged states, in addition to a sufficient number of frequencies depending on geometry complexity, for instance; two for a beam and three for an arch [37,38].…”

Crack identification in rods and beams under uncertain boundary conditions

“…The procedure is based on the so-called crack scanning method, recently proposed by the same authors, and on an improved Rayleigh's quotient type technique for calculating the crack induced changes in the natural frequencies. The detection of concentrated damage in more complex structures, such as parabolic arches or frames, by measured frequency variations has been approached in the papers by Pau et al [17], [9]. Caddemi and Caliò [2], [3] have recently developed a multiple crack damage identification procedure in beams based on closed form solutions of the free vibration problem.…”