A closed-form frequency equation of an arbitrarily supported beam with a transverse open crack considering axial–bending modal coupling

Abstract

This paper presents a closed-form frequency equation that predicts the modal coupling between the adjacent axial and bending modes of a beam with a transverse open crack. The final form of the proposed frequency equation is simply expressed in terms of the uncoupled frequency equations of intact and cracked beams for any type of support condition of the beam by introducing an axial–bending modal coupling factor. The validity of the proposed frequency equation is demonstrated through a comparison with the numerical results from a finite element analysis and with experimental data. For relatively deep cracks, the overall effect of axial–bending modal coupling on the axial modal frequencies is more significant than that on the bending modal frequencies.