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

Document Type : Research Article

Authors

Abstract

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.

Keywords

References

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