The vibration property of a rectangular-hollow-sectional beam with an external crack were theoretically and experimentally studied in this paper. The external part-through crack and through-thickness crack were considered. Linear elastic fracture mechanics were employed to establish the theoretical formula for computing the equivalent torsion spring stiffness of the two external cracks. Then, the experimental method of obtaining the equivalent torsion spring stiffness was developed. It is seen that the test data match fairly well with the analytical data. On this basis, the transfer matrix method was introduced to obtain the frequency equations of these cracked beams under three classic boundary conditions, and followed by the numerical method for calculating natural frequencies. Experimental tests on clamped–free beams were used to verify the accuracy. It should be noted that a part-through crack may lead to a more distinct natural frequency reduction than the through-thickness crack.
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