The crack location index for crack detection of a beam

Abstract

This study introduces a new index to be used for crack detection on a beam like structure. Our recent numerical modelling found sudden shifts in structural natural frequencies as a body with rotary inertia roving on a structure’s surface passes a crack. Theoretically, this phenomenon made it possible to locate the crack by observing the abrupt frequency change from the curve of natural frequency versus mass location. In practice, the mass is located at discrete positions thus the curve of natural frequency is not continuous. This led to the consideration of Δ𝑓 and Δ(Δ𝑓), where Δ𝑓 is the natural frequency change when the mass is located in two adjacent positions and Δ(Δ𝑓) is the change of Δ𝑓. The plots of Δ𝑓 or Δ(Δ𝑓) against mass location show peaks at the crack location and they could be highlighted. However, further study shows that the plots of Δ𝑓 or Δ(Δ𝑓) sometimes give false peaks, which makes it challenging to pinpoint the crack location This study aims to introduce a more robust index than Δ(Δ𝑓) that can suppress some of the false peaks, and hence the resulting curve can be more suitable for crack detection. We name it the crack location index. The crack location index was devised based on the participation of modal data in the expressions of natural frequency of a beam carrying a roving mass with rotary inertia and its derivative. They were demonstrated to be good candidates for locating the crack. The crack location index was applied to a numerical example of beam with a crack, and the crack location was pinpointed. It was shown that there were fewer false peaks in the curve of the crack location index than that of Δ(Δ𝑓).