Locating structural damage by detecting boundary effects

This paper presents a method of pinpointing structural damage locations using operational deflection shapes (ODSs) measured by a scanning laser vibrometer. The method assumes the form C-1 cos beta x + C-2 sin beta x + C-3 cosh beta x + C-4 sinh beta x for an ODS to match with its experimental data using a sliding-window least-squares method to determine the four coefficients C-i. It is shown that C-1 represents the central solution of displacement, C-3 the boundary-layer solution of displacement caused by boundary constraints, C(2)beta the central solution of slope, and C(4)beta the boundary-layer solution of slope. Moreover, C-1 * C-3 is Proportional to the difference of kinetic and elastic energy densities, C-3 - C-1 is proportional to the 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 structure and these coefficients change significantly at boundaries, crack locations are clearly revealed by the peaks on the C-1 * C-3 curve, Sign change 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 each of these coefficients requires a different length of data points for curve fitting in order to smooth the curve. Based on this different data length requirement and the peaks and sign change of these coefficients we derive a boundary effect detection (BED) method for finding damage locations. A non-linear sliding-window least-squares fitting technique is also derived for estimating the extent of structural damage. Numerical and experimental studies on beams with different damages have been performed to prove the accuracy and reliability of the BED method. (C) 2000 Academic Press.