Natural Vibration of a Beam with a Breathing Oblique Crack

An analytical method is proposed to calculate the natural frequency of a cantilever beam with a breathing oblique crack. A double-linear-springs-model is developed in the modal analysis process to describe the breathing oblique crack, and the breathing behaviour of the oblique crack is objectively simulated. The finite element method (FEM) analysis software ABAQUS is used to calculate the geometric correction factors when the cracked plate is subjected to a pure bending moment at different oblique crack angles and relative depths. The Galerkin method is applied to simplify the cracked beam to a single degree of freedom system, allowing the natural frequency of the beam with the breathing oblique crack to be calculated. Compared with the natural frequencies of the breathing oblique cracked beam obtained using the ABAQUS FEM method, the proposed analytical method exhibits a high computational accuracy, with a maximum error of only 4.65%