Effect of crack location and severity on modal parameters of a cantilever beam

One of the common methods of structural damage detections in structures is investigation of changes in modal parameters before and after damage. These methods which are mostly based on optimization techniques use an objective function based on natural frequencies and mode shapes. Success in detection of location and severity of the damage in these methods is severely a function of sensitivity of the objective function to the damage. As the objective function itself is function of natural frequencies or mode shapes or both of them, it is necessary that the sensitivity of modal parameters to damage location and severity is investigated. To this end, a cantilever beam is simulated numerically in this paper. Changing the location and severity of the damage, the effect of them on natural frequencies and mode shapes is studied. The results show that by increasing damage severity, natural frequencies decrease. On the other hand, moving the crack from the fix end to the free end of the cantilever beam, changes in the natural frequencies does not obey a specific pattern and for a crack of constant severity, decrement of natural frequencies from intact beam depends on the location of crack on the beam. Also it is observed that as the cracks approaches to the fix end, decrement of natural frequencies increased. The results show that the sensitivity of mode shapes to crack is low in beam. Therefore it is recommended to use natural frequencies or both natural frequencies and mode shapes together in objective functions.