Approximate Analytical Method for Damage Detection in Beam

Damage in structure alters its dynamic characteristics. The change is characterized by change in modal parameters i.e., modal frequencies. Mostly modal frequencies are used for monitoring the crack because modal frequencies are properties of the whole component. Thus vibration technique can be suitably used as a nondestructive test for testing crack detection of component. In this article efforts are made to develop a suitable method that can serve as a basis for 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. In theoretical analysis the crack is simulated by an equivalent axial spring, connecting the two segments of the beam. Analysis of this approximate model results in algebraic equation, which relates the natural frequencies of the beam and crack location. Also the relationship between the natural frequencies, crack location, and crack size has also 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 developed.