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Fractal Dimension Analysis of Higher-Order Mode Shapes for Damage Identification of Beam Structures

机译：梁结构损伤识别的高阶模态形的分形维分析

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摘要

Fractal dimension analysis is an emerging method for vibration-based structural damage identification. An unresolved problem in this method is its incapability of identifying damage by higher-order mode shapes. The natural inflexions of higher-order mode shapes may cause false peaks of high-magnitude estimates of fractal dimension, largely masking any signature of damage. In the situation of a scanning laser vibrometer (SLV) providing a chance to reliably acquire higher-order (around tenth-order) mode shapes, an improved fractal dimension method that is capable of treating higher-order mode shapes for damage detection is of important significance. This study proposes a sophisticated fractal dimension method with the aid of a specially designed affine transformation that is able to obviate natural inflexions of a higher-order mode shape while preserving its substantial damage information. The affine transformed mode shape facilitates the fractal dimension analysis to yield an effective damage feature: fractal dimension trajectory, in which an abruptly risking peak clearly characterizes the location and severity of the damage. This new fractal dimension method is demonstrated on multiple cracks identification in numerically simulated damage scenarios. The effectiveness of the method is experimentally validated by using a SLV to acquire higher-order mode shapes of a cracked cantilever beam.
机译：分形维数分析是一种基于振动的结构损伤识别的新兴方法。该方法中尚未解决的问题是其不能识别高阶模态形状的损坏。高阶模态形状的自然弯曲可能会导致高维分形维数估计的假峰值，从而大大掩盖了任何损坏迹象。在扫描激光振动计（SLV）提供可靠地获取高阶（大约十阶）模式形状的机会的情况下，能够处理高阶模式形状以进行损伤检测的改进的分形维方法非常重要。意义。这项研究提出了一种借助特殊设计的仿射变换的复杂的分形维数方法，该方法可以消除高阶模态形状的自然弯曲，同时保留其实质性的损坏信息。仿射变换模式形状有助于分形维数分析以产生有效的损伤特征：分形维数轨迹，其中突然冒险的峰值清楚地表明了损伤的位置和严重性。这种新的分形维数方法在数值模拟损伤场景下的多裂纹识别中得到了证明。通过使用SLV来获取裂纹悬臂梁的高阶模态形状，实验验证了该方法的有效性。

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  • 来源
    《Mathematical Problems in Engineering》 |2012年第8期|454568.1-454568.16|共16页
  • 作者

    Runbo Bai; Maosen Cao; Zhongqing Su; Wieslaw Ostachowicz; Hao Xu;

  • 作者单位

    Department of Engineering Mechanics, College of Water-Conservancy and Civil Engineering, Shandong Agricultural University, Taian 271000, China,Department of Engineering Mechanics, Hohai University, Nanjing 210098, China;

    Department of Engineering Mechanics, Hohai University, Nanjing 210098, China,Institute of Fluid Flow Machinery, Polish Academy of Sciences, 80-952 Gdansk, Poland;

    Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;

    Institute of Fluid Flow Machinery, Polish Academy of Sciences, 80-952 Gdansk, Poland;

    Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;

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