Abstract：In this paper, theoretical research on natural frequencies of cracked cantilever beams with a auxiliary mass are carried out. The transverse deflection of the cracked beam is constructed by adding a polynomial function, which represents the effects of a crack, to the polynomial function which represents the response of the intact beam. Then, the analytical formulation of the distribution of natural frequencies due to auxiliary mass over the beam is obtained through dynamics method. Through the analytical formulation the natural frequencies of the system change due to the roving of the mass along the cracked beam, which was called the natural frequencies curve(NFC). The NFC is shown to compare very well with those obtained using finite element method (FEM). In addition, due to the NFC contains the defect information of the beam, based on the NFC the damage on the beam can easily identify by using stationary wavelet transform (SWT). Finally, the influence to the natural frequency of the system, which caused by the quality block size, defect depth, defect location and other factors, is considered by using the analytical formulation in this paper. The results show the reliability of the theoretical derivation and the accuracy of damage identification.
2016, Vol. 37 
