The use of quasi-isospectral operators for damage detection in rods

We consider the inverse problem of reconstructing the axial stiffness of a damaged rod from the knowledge of a finite number of resonant frequencies of the free axial vibration under supported end conditions. The damage is described as a reduction of the axial stiffness, and the undamaged and damaged configurations of the rod are assumed to be symmetric. The method is based on repeated determination of quasi-isospectral rod operators, that is rods which have the same spectrum of a given rod with the exception of a single resonant frequency which is free to move in a prescribed interval. The reconstruction procedure is explicit and it is numerically implemented and tested for the identification of single and multiple localized damages. The sensitivity of the technique to the number of frequencies used and to the shape, intensity and position of the damages, as well as to the presence of noise in the data, is evaluated and discussed. The effect of suitable filtering of the results based on a priori information on the physics of the problem is proposed. An experimental application to the identification of localized damage in a free-free steel rod is also presented.