Using incomplete FRF measurements for damage detection of structures with closely-spaced eigenvalues

In this paper, a new model updating-based damage detection method based on a modified sensitivity equation is proposed that can tackle the problem of damage detection in structures with closely-spaced eigenvalues. It is known that modal information, such as natural frequencies, in these structures can be of close proximity, making the procedure of damage detection hard if not impossible. The obtained sensitivity equation uses incomplete measurements from frequency response functions (FRFs) to conduct the challenging damage detection of structures with closely-spaced eigenvalues. Although using FRF for damage detection of this kind of structures can offer some advantages over modal data, there are still some challenges that need to be addressed. For instance, it is not possible to have the response of the structure measured in all of its degrees of freedom. As such, the proposed FRF-based model updating method is capable of overcoming these limitations and has the advantage of avoiding modal analysis errors. In order to evaluate the efficiency of the proposed method, two numerical examples of a 144-element three-layered laminated composite plate and a 120-element three-dimensional truss structure, as examples of structures with closely-spaced eigenvalues, are studied. The results demonstrate the capability of the proposed method in damage detection of structures with closely-spaced eigenvalues with incomplete measurement data. Moreover, the results of comparison between the proposed method with some other methods demonstrate the superiority of the proposed method in damage detection of structures with closely-spaced eigenvalues using noisy incomplete FRF data.