The Surface Interpolation Method for damage localization in plates

This paper presents a vibration based procedure for locating reductions of stiffness in plate-like structures. This procedure is a generalization to the two-dimensional case of the Interpolation Method (IM) previously published by the author. The method is based on the definition of a damage sensitive feature in terms of the accuracy of a spline function in interpolating the operational displacement shapes of the structure. In the previous works the IM was applied as a method of level 2 for damage identification that is able to detect and localize damage. In this paper an analytical relationship between the damage feature and the curvature discontinuity is proved. For two-dimensional structures, a bi-cubic spline surface is defined herein to interpolate the operational shapes. In order to account for the uncertainties related to random variations of the damage feature, an approach based on the definition of an acceptable value of the probability of false alarm was formerly proposed by the author. A simplified version of the algorithm is presented herein for the case whereby the statistical distribution of the damage feature in the original (undamaged) state is not available, and the damage diagnosis has to be carried out based on just two sets of responses recorded on the original and on the (possibly) damaged structure. The proposed two-dimensional Surface Interpolation Method (SIM) is checked herein via numerical simulations using the FE model of a plate and modeling local reductions of stiffness through a reduction of the elastic modulus of the material. Results demonstrate that the algorithm provides a reliable tool for damage identification of plate-like structures. The performance of the method can be affected by noise in recorded data, however a careful choice of the accepted probability of false alarm can reduce this drawback.