Numerical, statistical and experimental investigation on damage quantification in beams from modal curvature

Abstract

In the task of locating and quantifying damage in beams from experimentally-obtained modal data, one-dimensional models are attractive due to their simplicity and apparent generality. However, stress concentration and neutral axis change near cracks make the assumptions of classical beam theory invalid. Notwithstanding, empirical equivalences with some analytical basis have been stated in the past, which led to some successes in detection and localization, although with uncertain grade of generality in quantification. In the present work, a method for quantifying damage in simply supported beams from modal curvature is analytically developed, highlighting the hypotheses upon which it relies. Then, a wide variety of cases (thousands) are parametrically modeled by using solid finite elements. The considered universe involves different materials; section types; crack locations, positions and sizes; sensor positions and locations; and beam dimensions. From the modal analysis results, damage indicators that are based on modal curvature are tested for their damage-quantification capability. Finally, this large data set is statistically assessed by using data mining techniques. Thus, interesting conclusions are found about the limitations and advantages of this damage-quantification method. Also, useful recommendations are provided for defining suitable positions and locations of sensors in beams. Finally, a series of experimental tests demonstrates the performance of the method under non-ideal conditions.