Investigating the modal behaviors of a beam with a transverse crack on a high-frequency bending node

Abstract

There is a premise that the reduction of the bending modal frequency does not occur in the presence of a transverse crack on the bending node of a beam. This study investigated the modal behaviors of a beam with a transverse crack on a bending node and revealed that this premise does not hold, particularly for a deep crack on a high-frequency bending node. Mode II crack (sliding crack mode) of fracture mechanics, which has not been considered in most previous studies, was found to cause the reduction of the modal frequency of a beam with a crack on a bending node. A new frequency equation that accounts for mode II crack was devised. The implications of the new frequency equation were demonstrated through the normalized modal frequency shift factor. Further, the validity of the proposed frequency equation was demonstrated by comparing the quantitative results with finite element analysis results and experimental data.