The effect of a crack near the fixed end on the natural frequencies of a cantilever beam
The paper examines how a transverse crack near the fixed end of a beam affects the natural frequency drop. It is known that the decrease in the frequency due to a crack depends on the position of the damage and its severity. This happens because the slice of the beam on which the crack is located changes its stiffness. Consequently, the damaged beam is no longer able to store the identical amount of energy as the healthy one. In addition, the field of stresses and deformations on an extended
... s on an extended area around the crack is disturbed. This alteration can manifest freely for most positions of the crack along the beam. For this case, there is a direct relationship between the defect position and the frequency change, given by the modal curvature of the beam. Close to the fixed end, the field of stress and deformation is hindered on one side of the crack by the fixed end condition. In this way, the crack will produce a lower frequency drop compared with what it is expected. We performed simulations to obtain the frequency drop if the crack is located very close to the fixed end. With these values, we plot the regression curve and estimate the frequencies which should result for a crack located exactly on the fixed end of the beam if symmetric fields of stress and strain are possible. The results are necessary because the frequency drop characterizes the damage severity, further used in the damage detection processes.