Approximate analytical method for damage detection in free–free beam by measurement of axial vibrations

Nowadays, sophisticated structures and machinery parts are constructed by using metallic beams. Beams are widely used as structural element in civil, mechanical, naval, and aeronautical engineering. In structures and machinery, one undesirable phenomenon is crack initiation in which the impact cannot be seen overnight. Cracks develop gradually through time that lead finally to catastrophic failure. Therefore, crack should be monitored regularly with more care. This will lead to more effective preventive measure and ensure continuous operation of the structure and machine. Damage in structure alters its dynamic characteristics. The change is characterized by change in modal parameters, that is, modal frequencies. Thus, vibration technique can be suitably used as a nondestructive test for crack detection of component to be tested. Mostly modal frequencies are used for monitoring the crack because modal frequencies are properties of the whole structure component. In this paper, efforts are made to develop suitable methods that can serve as the basis to detection of crack location and crack size from measured axial vibration data. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure. The method is based on measurement of axial natural frequencies, which are global parameter and can be easily measured from any point on the structure and also indeed, the advantage in modeling complexity. In theoretical analysis, the relationship between the natural frequencies, crack location, and crack size has been developed. For identification of crack location and crack size, it was shown that data on the variation of the first two natural frequencies is sufficient. The experimental analysis is done to verify the practical applicability of the theoretical method