Identification of a crack in I-beams based on wavelet finite element method

The forward and inverse problems in crack identification of I-beams are studied. The forward problem is to determine the first three natural frequencies of the cracked beam given the location and size of the crack and the inverse problem is to determine the location and size of the crack given the first few natural frequencies of the cracked I-beam. By taking the cracked rail with I cross-section as an example, the model of the beam based on wavelet finite element methods is constructed and the first three natural frequencies are obtained. The crack is modeled as a rotational spring. A fast algorithm of inverse problem is presented which transforms the vibration frequency equation into the quadratic equation with only one unknown parameter, the rotational spring stiffness, by the determinant transformation method. Then the graphs of crack depth versus crack location are plotted for each natural frequency. The point of intersection of the curves gives the location and size of the crack. The experimental example indicates that the current method is effective and accurate. This study provides a new method for the prognosis and diagnosis of cracks in I-beam structures.