Structural Damage Identification Using Mode Shape Slope and Curvature

Mode shape-based structural damage detection is an emerging field of research. This study presents a vibration-based damage localization technique using the derivatives of mode shapes corresponding to undamaged and damaged states of a structure. First, mathematical expressions of the derivatives of mode shapes have been formulated and correlated with the damage location. The mathematical derivation shows that the difference in mode shape slopes attains a Dirac delta function at the location of the damage. Also, the difference in mode shape curvature is discontinuous at the damage location. However, it attains extreme values around the damage location. For illustration purposes, simulation studies on a shear building have been carried out to show the derivatives of the first few mode shapes to be sensitive to the damage location. An experimental case study involving a shake-table test has also been performed on a miniature model of a 6-story steel frame to investigate the efficiency of the proposed technique in real situations. Therefore, the mathematical formulation followed by the numerical study as well as the experimental investigation shows the competence of the proposed approach in structural damage identification. (C) 2017 American Society of Civil Engineers.