Investigation of Vibration Behavior and Crack Detection of a Cracked Short Cantilever Beam under the Axial Load

In this research, firstly, the vibrational behavior of a cracked short cantilever beam under the axial load is investigated, and then, an analytical approach for the crack identification based on the vibration analysis is proposed. The cracked section of the beam is considered as a flexible element, which divides the beam into two segments. Using the fracture mechanics theory, the local flexibility of the crack is modeled as a mass-less tensional spring. By applying the boundary conditions and the inner conditions at the crack location, and taking into account the effects of shear deformation and rotary inertia, the governing equation of motion for the cracked beam is derived. The influence of the axial load and the crack parameters on the vibration behavior of the cracked beam is studied by establishing and solving the corresponding eigenvalue problem, directly. Then in order to predict the crack depth and location through the known natural frequencies of the cracked beam, which are obtained by the experimental tests, the corresponding inverse problem is established and solved analytically. The Results have been validated by the experimental and theoretical data reported in the literatures.