Locating structural damage by detecting boundary effects

This paper presents a method of pinpointing structural damage locations usi ng operational deflection shapes (ODSs) measured by a scanning laser vibrom eter. The method assumes the form C-1 cos beta x + C-2 sin beta x + C-3 cos h beta x + C-4 sinh beta x for an ODS to match with its experimental data u sing a sliding-window least-squares method to determine the four coefficien ts C-i. It is shown that C-1 represents the central solution of displacemen t, C-3 the boundary-layer solution of displacement caused by boundary const raints, C(2)beta the central solution of slope, and C(4)beta the boundary-l ayer solution of slope. Moreover, C-1 * C-3 is Proportional to the differen ce of kinetic and elastic energy densities, C-3 - C-1 is proportional to th e curvature, and C-4 - C-2 is proportional to the spatial derivative of the curvature. Because cracks on a structure introduce new boundaries to the s tructure and these coefficients change significantly at boundaries, crack l ocations are clearly revealed by the peaks on the C-1 * C-3 curve, Sign cha nge of C-4, peaks on the fitting error curve, and sudden changes of C-3 - C -1 and C-4 - C-2. Moreover, numerical and experimental results show that ea ch of these coefficients requires a different length of data points for cur ve fitting in order to smooth the curve. Based on this different data lengt h requirement and the peaks and sign change of these coefficients we derive a boundary effect detection (BED) method for finding damage locations. A n on-linear sliding-window least-squares fitting technique is also derived fo r estimating the extent of structural damage. Numerical and experimental st udies on beams with different damages have been performed to prove the accu racy and reliability of the BED method. (C) 2000 Academic Press.