Damage detection in vibrating beams, or beam systems, is dealt with in this paper. Damage is represented by a more or less concentrated decrease in stiffness. A linear behavior is assumed before and after the damage. A peculiar aspect of damage detection, at times neglected, is that damage is frequently concentrated in a few zones, albeit unknown, so that only the modification in the characteristics of a few sections or elements needs to be determined. Attention is focused on the basic aspects of the problem, by discussing the amount of frequencies necessary to locate and quantify the damage uniquely. Two different procedures of damage identification are used, which mainly take advantage of the peculiar characteristics of the problem. Cases with pseudoexperimental and experimental frequencies are solved. A generalization of the procedure based on finite-element models, which makes possible the tackling complex structural cases, is illustrated and discussed with some examples.

The paper focuses on the problem of locating and quantifying damage in vibrating beams due to cracks. The problem is shown to have certain peculiarities that, to some extent, make it easier to solve than classical situations of structural identification. The solution of the problem is based on the minimization of the objective function that compares analytical and experimental data. A fairly general automated procedure is developed using a finite element code as a routine to evaluate modal quantities. The data necessary to locate and quantify damage correctly are discussed. General considerations lead to the conclusion that at least one measurement more than the expected number of cracked sections is necessary to obtain a unique solution. The procedures developed are applied to the study cases: a supported beam and a clamped beam with one or two cracks, using both simulated and experimental data. Satisfactory results are obtained. Although only beams were considered, the methodology developed can be extended to any kind of framed structure.