Publications

Non-model-based damage identification of plates using principal, mean and Gaussian curvature mode shapes

Xu, Yongfeng X.; Zhu, Weidong Z.; Smith, Scott A.

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; the method is applicable and robust to MSs associated with low and high elastic modes on dense and coarse measurement grids. 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, provided that the undamaged plate has a smooth geometry and is made of material that has no stiffness and mass discontinuities. 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. A MS of an aluminum plate with damage in the form of a machined thickness reduction area was measured to experimentally investigate the effectiveness of the proposed CDIs in damage identification; the damage on the plate was successfully identified.