Determination of Structural Flaws in Beams

A nondestructive experimental technique for determination of structural flaws in cantilever beams is presented. The proposed method is capable of detecting location of cracks and other possible structural flows on a beam using its natural frequencies and vibration mode shapes measured on a roving mass on the beam. To verify the validity of the proposed method, vibration response of a cracked cantilever beam with a stationary roving mass is investigated. The beam is modeled as an Euler-Bernoulli beam with rectangular cross section. The axial and transverse deformations of the cracked beam are coupled through a stiffness matrix determined using the fracture mechanics principles. The developed model is used to determine analytical solutions for the variation of natural frequencies and mode shapes of a cracked cantilever beam versus the position of the roving mass. The analysis indicates that the variation of the natural frequencies versus position of the roving mass can drastically change when the roving mass is close to the position of a flaw. Moreover, the effects of the location and depth of the crack, the location and the weight of the roving mass on the natural frequencies, and mode shapes of the beam are investigated. The analytical results show that the coupling between the axial and transverse vibrations for moderate values of crack depth and/or roving mass is weak. Increasing the crack depth, the mass and the rotary inertia increases the coupling effect.

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