Free vibration characteristics of an elastic simple beam with a fatigue notch crack damage located any where of the beam is investigated. The notch crack is modeled by an elastic torsion spring whose stiffness is taken to be finite and is determined from fracture mechanic theory. On the assumption that the crack is always open when the beam vibrates transversely, the motion equation and the boundary conditions of a simple-supported beam with a crack located anywhere of the beam is deduced. The first-order to the sixth-order frequencies varying with the crack depth and the crack location are calculated.
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