Structural damage detection methods relying on laser-measured vibration shapes have become a research focus in the past decade. For damage in a beam/bar with reduced cross-sectional dimensions, such as a notch, it causes changes in both its bending stiffness and axial stiffness in the damage region. Such stiffness changes can induce discontinuities in derivatives of flexural and longitudinal vibration shapes, whereby the damage can be detected and located. Derivatives of flexural vibration shapes have been widely used for structural damage detection, whereas derivatives of longitudinal vibration shapes were recently proposed for structural damage detection and have attracted much less attention. Although it is difficult to excite and measure longitudinal vibration, it can be useful for detecting damage in such a structure as a cable, since flexural vibration of the cable is mainly governed by its tension and not its bending stiffness. In this study, capabilities of derivatives of laser-measured flexural and longitudinal vibration shapes in structural damage detection are comprehensively compared. In particular, to overcome their common deficiency of being susceptible to environmental noise interference, the multiscale analysis based on wavelet transform is integrated into derivatives of vibration shapes to enhance their robustness against noise interference. Analytical and experimental validation shows that compared with commonly used derivatives of flexural vibration shapes, derivatives of longitudinal vibration shapes have the same capability in detecting damage in beam/bar-type structural components.

中文翻译：

---

使用激光测量弯曲和纵向振动形状的导数进行结构损伤检测的比较研究

依靠激光测量振动形状的结构损伤检测方法已成为过去十年的研究热点。对于横截面尺寸减小的梁/杆中的损坏，例如缺口，它会导致损坏区域的弯曲刚度和轴向刚度发生变化。这种刚度变化会导致弯曲和纵向振动形状的导数不连续，从而可以检测和定位损坏。弯曲振动形状的导数已广泛用于结构损伤检测，而纵向振动形状的导数最近被提出用于结构损伤检测，但引起的关注却少得多。虽然很难激发和测量纵向振动，但它可用于检测电缆等结构中的损坏，因为电缆的弯曲振动主要受其张力而不是其弯曲刚度控制。在这项研究中，综合比较了激光测量弯曲和纵向振动形状的导数在结构损伤检测中的能力。特别是为了克服它们普遍易受环境噪声干扰的不足，将基于小波变换的多尺度分析集成到振动形状的导数中，以增强其对噪声干扰的鲁棒性。分析和实验验证表明，与常用的弯曲振动形状的导数相比，纵向振动形状的导数在检测梁/杆型结构部件的损坏方面具有相同的能力。