Fundamental mode shape and its derivatives in structural damage localization
Fundamental mode shape and its derivatives in structural damage localization
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DOI：
10.1016/j.jsv.2013.05.003
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发表时间：
2013-10
影响因子：
4.7
通讯作者：
K. Roy;S. Ray‐Chaudhuri
中科院分区：
文献类型：
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作者：
K. Roy;S. Ray‐Chaudhuri
在过去的几十年中，各种涉及模态参数的结构损伤检测技术得到了广泛的应用。这是因为结构的模态参数可以很容易地从强迫、自由或环境振动测量中获得。在许多这些技术中，模态曲率已被用于损伤定位。在本文中，提供了一个数学基础，以显示结构损伤和基本振型及其衍生物的变化之间的相关性。这是通过利用摄动方法推导受损模态的表达式来实现的。对于悬臂剪切梁，离散成大量的元素，这种方法表明，由于任何损伤的基本模式形状的变化是一个很好的指标损伤局部化，因为它被发现是不连续的损伤位置。此外，高阶导数的变化（即，斜率和曲率）的基本振型被证明是足够敏感的损伤定位。一个剪力型建筑和一个钢框架的数值算例表明了该方法在损伤定位中的有效性。从这项研究中已经发现，样条拟合的振型在有限的自由度的情况下，这是通常采用的绘制振型及其衍生物，可能会导致错误的损伤检测。
Various techniques for structural damage detection involving modal parameters have widely been used over the past few decades. This is because the modal parameters of a structure can easily be obtained from forced, free or ambient vibration measurements. In many of these techniques, mode shape curvature has been used for localization of damage. In this paper, a mathematical basis is provided to show the correlation between a structural damage and a change in the fundamental mode shape and its derivatives. This has been achieved by deriving the expression of a damaged mode shape utilizing a perturbation approach. For a cantilever shear beam, discretized into a large number of elements, this approach demonstrates that the change in the fundamental mode shape due to any damage is an excellent indicator of damage localization as it is found to be discontinuous at the location of damage. Further, the change in higher derivatives (i.e., slope and curvature) of the fundamental mode shape is shown to be sensitive enough in damage localization. A numerical study involving a shear building and a steel moment-resisting frame is conducted to show the effectiveness of the proposed approach in damage localization. It has been found from this study that spline fitting of mode shapes in case of a limited number of degrees-of-freedom, which is generally adopted for plotting mode shapes and their derivatives, may lead to false detection of damage.