Crack detection in beams from the differences in curvature mode shapes

Abstract

A crack in a structure alters its dynamic characteristics. The change is characterized by changes in the eigen parameters, i.e., natural frequency and the mode shapes associated with each natural frequency. Considerable effort has been spent in obtaining a relationship between the changes in eigen parameters, the crack location and the crack size. Most of the emphasis has been on using the changes in the natural frequencies and the damping values to determine the location and the size of the crack. In this paper curvature mode shape is used as a possible parameter for identifying and locating crack in a structure. By using a cantilever and a simply supported beam model, it is shown here that the absolute changes in the curvature mode shapes are localized in the region of crack and hence can be used to detect crack in a structure. The changes in the curvature mode shapes increase with increasing size of crack. This information can be used to obtain the amount of crack in the structure. ANSYS software was used to obtain the displacement mode shapes of the model. By using a central finite difference approximation, curvature mode shapes were then calculated from the displacement mode shapes. It can be seen that the maximum difference value for each mode shape occurs in the crack location.