This paper presents an enhanced method to locate and quantify damage in beam-like structures using changes in deflections estimated from modal flexibility (MF) matrices. The method is developed from explicit relationship between a series of MF-based deflection change vectors and the damage characteristics. Based on this, three damage locating criteria are defined and used to detect and locate damage. Once the damage is located, its severity is estimated conveniently from a closed-form function. The capability of the proposed method is examined through numerical and experimental verifications on a steel beam model. The result shows that the method accurately locates and quantifies damage under various scenarios using a few modes of vibration, with satisfactory or even better results compared to those obtained from traditional static deflection-based method. The performance of the proposed method is also compared with three well-known vibration-based damage detection methods using changes in MF and modal strain energy. It is found that the proposed method outperformed the other three methods, especially for multiple damage cases. As beams can represent various structural components, the proposed method provides a promising damage identification tool targeting the application to real-life structures.

中文翻译：

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使用基于模态柔度的挠度变化定位和量化梁状结构中的损伤

本文提出了一种增强的方法，使用从模态柔度 (MF) 矩阵估计的挠度变化来定位和量化梁状结构中的损伤。该方法是从一系列基于 MF 的挠度变化矢量与损伤特性之间的显式关系发展而来的。在此基础上，定义了三个损伤定位标准并用于检测和定位损伤。一旦确定损坏位置，就可以方便地从封闭形式的函数中估计其严重程度。通过对钢梁模型的数值和实验验证来检验所提出方法的能力。结果表明，该方法使用几种振动模式准确地定位和量化了各种场景下的损伤，与传统的基于静态偏转的方法相比，具有令人满意甚至更好的结果。所提出的方法的性能也与三种众所周知的基于振动的损伤检测方法进行了比较，该方法使用 MF 和模态应变能的变化。结果发现，所提出的方法优于其他三种方法，特别是对于多个损坏情况。由于梁可以代表各种结构部件，因此所提出的方法提供了一种很有前途的损伤识别工具，旨在应用于现实生活中的结构。