9. Non-Model-Based Damage Identification of Plates Using Curvature Mode Shapes

Mode shapes (MSs) have been extensively used to identify structural damage. This paper presents a new non-model-based method that uses principal, mean and Gaussian curvature MSs (CMSs) to identify damage in plates. A multi-scale discrete differential-geometry scheme is proposed to calculate principal, mean and Gaussian CMSs associated with a MS of a plate, which can alleviate adverse effects of measurement noise on calculating the CMSs. Principal, mean and Gaussian CMSs of a damaged plate and those of an undamaged one are used to yield four curvature damage indices (CDIs), including Maximum-CDIs, Minimum-CDIs, Mean-CDIs and Gaussian-CDIs. Damage can be identified near regions with consistently higher values of the CDIs. It is shown that a MS of an undamaged plate can be well approximated using a polynomial with a properly determined order that fits a MS of a damaged one. New fitting and convergence indices are proposed to quantify the level of approximation of a MS from a polynomial fit to that of a damaged plate and to determine the proper order of the polynomial fit, respectively. The proposed method is numerically applied to MSs of an aluminum plate with damage in the form of a thickness reduction area to investigate its effectiveness; the damage on the plate is successfully identified.