基于模态曲率相关性分析的结构损伤定位方法研究

基于对灰色相关性分析在结构损伤中的已有研究，对基于灰色模态曲率相关性分析的动力损伤识别技术进行了深入研究，首次提出了基于一阶振型数据的损伤定位敏感因子一模态曲率置信因子（MDCAC），通过该参数的变化曲线，就可以根据不同节点在损伤前、后的模态曲率因子的大小实现对结构的损伤定位。通过悬臂梁的数值分析，验证了模态曲率置信因子（MDCAC）是一个对损伤极为敏感的参数，该参数不仅对单损伤可以准确定位，对于相邻的多损伤、不相邻的多损伤都可以精确识别，即使是小到1％的微损伤也可以通过该参数的变化曲线对损伤单元准确识别。运用该因子进行损伤定位时，只需结构的一阶振型数据，而且不论数据量的多少，该因子都能对损伤单元进行准确的定位，因此该方法在大型结构及复杂结构的损伤识别中具有广阔的应用前景。

THE RESEARCH ON DAMAGE LOCALIZATION USING MODAL CURVATURE

Based on the research of the application of the grey relation analyses on the damage localization, a new structural damage localization method using the first order modal displacement based on grey modal curvature relation coefficient is proposed in this paper. The grey modal displacement curvature assurance coefficient （MDCAC） is defined and used to locate damage in the structure; the damage element can be located correctly according to the value of MDCAC. A numerical example of a cantilever beam with single or multiple damages is used to examine the capability of the proposed grey-theory-based method to localize damages. The numerical results show that the damage in the structure could be localized correctly through using the modal displacement curvature coefficient, regardless of the number of measured modal displacement nodes. This proposed method only requires first order modal displacement, which is easily available in practice, and has wide applications in damage detection of large-scale structure.