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.
Many approaches on modeling of cracks in structural members have been reported in the literatures. However, most of them are explicitly developed for the purpose of studying the changes in static and dynamic responses of the structure due to the crack damage, which is a forward problem mathematically. Thereby the use of these models is inconvenient or even impossible for detecting damage in structures from vibration measurements, which is usually an inverse problem. An anisotropic damage model is proposed in this paper for detecting edge-parallel cracks in a rectangular thin plate. The cracked plate element is represented by an equivalent plate element with orthotropic anisotropic material expressed in terms of the virgin material stiffness and a tensor of damage variables. A non-model-based damage identification approach is developed incorporating the proposed anisotropic model and the estimated uniform load surface curvature (ULSC) of the plate from vibration measurements. The actual length of the crack is then predicted from the identified variables based on conservation law of potential energy for crack growth. The validity of the methodology is demonstrated by numerical examples and experiment results with comparison with results from existing crack identification theory.