Predicting the Modal Frequencies of a Cracked Beam Considering Crack Modes I and II

Abstract

Surface-mounted piezoelectric wafers allow for the evaluation of the dynamic characteristics of a cracked beam in the high-frequency range. The modal coupling between the adjacent axial and bending modes of the cracked beam was observed in the high-frequency range. The modal frequencies do not change in the low-frequency range owing to a crack located on the bending node of an intact beam. However, mode II crack causes a reduction in modal frequencies, particularly in the high-frequency range, in the presence of the crack on the bending node. When a crack is arbitrarily located on a beam, modal frequencies in the high-frequency range are simultaneously affected by mode I crack, which is associated with the axial-bending mode coupling, and mode II crack. The effect of mode I crack on the reduction in the modal frequency is dominant, except for the crack on the bending node. Mode II crack became more sensitive to the reduction in the modal frequency as the mode number increased. Therefore, crack modes I and II should be taken into account simultaneously for the accurate prediction of the modal frequency, which enables reliable crack diagnosis of a beam. In this study, the modal frequencies of cracked beams were predicted by considering both crack modes I and II. The characteristic equations of the cracked beam were derived from the compatibility equation corresponding to crack modes I and II, equilibrium equations, and boundary conditions. The modal frequencies calculated from the characteristic equations were verified through a comparison with the finite element analysis and experimental results.