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基于振动特性的损伤识别方法是研究者十分关注的问题。为了确保这类方法的有效性,有必要研究振动特性对结构损伤的敏感性。为此,该文推导了有一处损伤的悬臂梁的振动特性的解析解,并在此基础上详细讨论了不同的振动特性对损伤的敏感性。分析结果表明:当梁中某段存在损伤时,结构的频率和模态不会发生太大的变化;而转角模态和曲率模态在损伤区域会发生明显的突变。这些结果以及文中的讨论对相关领域的研究者有一定的参考价值。
The damage identification method based on vibration characteristics is a very important issue for researchers. In order to ensure the validity of these methods, it is necessary to study the sensitivity of vibration characteristics to structural damage. For this reason, the paper derives an analytic solution of the vibration characteristics of a cantilever beam with damage, and on this basis, discusses the sensitivity of different vibration characteristics to damage. The analysis results show that the frequency and mode of the structure will not change much when there is damage in one section of the beam, while the rotation mode and the curvature mode of the beam will obviously change in the damaged area. These results, as well as the discussion in this paper, have certain reference value for researchers in related fields.