Some theoretical and experimental studies on beams for identification of crack location and magnitude by measurement of natural frequencies

Abstract

In this thesis, theoretical and experimental analysis of vibrating beam having various boundary conditions with crack is carried out. 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 natural frequencies of cracked beam for transverse as well as longitudinal vibration, which are global parameter and can be easily measured from any point on the beam. In theoretical analysis the crack is simulated by an equivalent 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 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 computation of natural frequencies of uncracked and cracked beam is facilitated by ANSYS FEM package. This database is to be utilized in analytical method to address the inverse problem to identify the crack location and crack size. Experiments have also been performed on beams having various boundary conditions. The experimental analysis is done to verify the practical applicability of the theoretical method developed. A good agreement between the predicted and actual crack location and crack size is obtained. The results obtained by experimentally are compared with the results obtained by theoretically. The results are given in the form of tables. Also the results are compared in the form of graphs.