Identification of crack location and magnitude in a cantilever beam from the vibration modes

Measurement of flexural vibrations of a cantilever beam with rectangular cross-section having a transverse surface crack extending uniformly along the width of the beam and analytical results are used to relate the measured vibration modes to the crack location and depth. From the measured amplitudes at two points of the structure vibrating at one of its natural modes, the respective vibration frequency and an analytical solution of the dynamic response, the crack location can be found and depth can be estimated with satisfactory accuracy. The method can be used to identify cracks in structures by measuring its modal characteristics. It is a non-destructive testing method for crack identification, and it is applicable to structures for which a structural analysis is available. The main features of the method are as follows: (a) it requires amplitude measurements at two positions of the structure only; (b) it is applicable to all one-dimensional structures; (c) it demands modest computational effort; (d) it is an accurate, simple and easy to handle method having the advantage that the measurements may be carried out in situ with rather simple equipment.