中文摘要：

论文研究了辅助质量块单裂纹悬臂梁耦合系统的固有频率，用无缺陷悬臂梁固有振型叠加一个多项式来近似拟合含单裂纹悬臂梁的振型，由动力学方法推导了辅助质量块一单裂纹悬臂梁系统的固有频率方程的解析形式，系统频率随着质量块在梁上位置改变而改变，即可得到固有频率曲线，此频率曲线包含了缺陷信息，因此可对固有频率曲线进行平稳小波变换来识别梁上的缺陷．同时用有限元计算结果对上述固有频率理论推导进行验证，有限元结果与论文理论推导结果相一致．最后论文数值计算了质量块大小、缺陷深度、位置等因素对系统固有频率的影响，也探讨了平稳小波变换用于识别损伤，结果验证了该理论推导的可靠性和损伤识别的准确性．

英文摘要：

The natural frequencies of cracked cantilever beams with an auxiliary mass are derived theo retically in the present work. The transverse deflections of cracked beams are constructed by adding a polynomial function in representation of the effects of a crack to the polynomial function describing the response of an intact beam. The analytical formulation of the distribution of natural frequencies due to auxiliary mass over the beam is obtained. The natural frequencies of the mass-beam system change due to the roving of the mass along the cracked beam, which is called the natural frequencies curve （NFC）. The NFC obtained using the theoretical formulation has good agreement with the one using the finite element method （FEM）. In addition, because the NFC contains defect information of the beam, the damage on the beam can be easily identified using stationary wavelet transform （SWT）. Finally, the influence of defect depth and defect location on the natural frequency of the mass-beam system is considered using the analytical formulation. The results demonstrate the reliability of the theoretical derivation and the accuracy of the damage identification.