Damage localization in plate structures from flexibility and its derivatives

The purpose of this study is to search for an efficient flexibility-based method for locating damage in plate structures. Although a large number of methods exist for detecting damage in a structure using measured modal parameters, many of them require a correlated finite element model. In this paper several damage localization methods based on changes in the modal flexibility, Uniform Load Surface (ULS), and their curvatures will be discussed. These methods require frequencies and mode shapes from the lower modes of the plate before and after damage, or only the eigen-pairs from the damaged state if the gapped-smoothing technique is applied. The method based on flexibility changes or flexibility curvature was originally proposed to localize damage in one-dimensional beam-like structures. In this paper this technique is generalized to two-dimensional plate structures using Chebyshev polynomial approximation, and incorporated with ULS, the derivative of modal flexibility, and its curvature for detecting damage in plates. Numerical examples considering measurement noise, mode truncation, and sensor sparsity are studied to evaluate and compare the effectiveness of the proposed methods. It is found that the ULS curvature is the most sensitive index for locating damage, especially for truncated and noisy measurements.