Modal analysis of a beam with bilateral breathing oblique cracks

Abstract

In this paper, a theoretical method is proposed to conduct the modal analysis of a beam with bilateral breathing oblique cracks. Based on the principle of Virtual Work, the oblique crack is transformed into the local flexibility. Considering the breathing behavior of bilateral oblique cracks, the trigonometric interpolation function is used to simulate the stiffness variation of cracked beam. Galerkin method is applied to simplify the vibration differential equation of the beam to several single degree of freedom systems, and natural frequencies and mode shapes of the cracked beam can be obtained easily. Compared with the numerical simulation method, the theoretical method proposed can be verified. Example analysis shows that the inclined angle of oblique crack is also an important factor for the modal of cracked beam, and breathing model of bilateral cracks is quite different from that of bilateral open cracks.