中文摘要：

针对梁在裂纹尖端附近存在奇异性的现象，将谱元法和断裂力学方法相结合，推导了谱元梁单元、裂纹单元的刚度方程。谱元法在求解结构的振动响应时，由于采用的是与频率相关的插值函数，因此理论上可以获得精确的频域解；利用该方法，建立了基于谱元法的裂纹悬臂梁模型，通过求解裂纹梁的前三阶固有频率，并利用曲面拟合技术绘出固有频率的解曲面，从而可以很方便的诊断出裂纹参数。利用该检测方法对悬臂梁结构进行了裂纹识别数值研究，结果表明，该方法具有简单，求解速度快，精度高的优点；不仅能准确的识别出悬臂梁的损伤位置，还能定性地识别裂纹损伤的程度。

英文摘要：

Focusing on the singularity phenomenon near the cracked tip, the spectral element method combining with fracture mechanics was proposed, and the element stiffness matrices of the spectral beam element and the crack element were derived. The spectral element method （SEM） is based on the frequency-dependent interpolation functions. Theoretically, the exact frequency-domain solution to the structural dynamic response can be obtained by using the spectral element method. The SEM was applied to the crack diagnosis of structures by modeling the canti- lever beam with the crack. Then according to the obtained first three natural frequencies of the cracked beam, the solution surface was plotted by adopting the solution surface fitting technology. Subsequently, the crack parameter can be readily obtained. Numerical cases on a cantilever beam for crack detection based on the proposed method was conducted. It has been shown that the present method demonstrates its advantages in regard simplicity, fast solving speed and high precision. So the present method has not only the ability to to the aspects of identify the loca- tion of the damage to the beam structures, but also has the ability to predict the extent of the damage qualitatively.