Abstract In this paper, a method for crack detection in beams is proposed by applying the concept of defect modes in band gaps of imperfect phononic crystals (PCs). In the proposed crack detection method, a periodic array of concentrated masses is attached on a straight beam to generate the Bragg band gaps. Then, a crack in the beam might induce the defect modes in some of the band gaps, whose frequency depends on the periodicity of the concentrated masses or the location and size of the crack. With the spectral element method formulation, we first study the influence of the concentrated masses on the bandgap formation. Then, we study the influences of the lattice constant or the size and location of the crack on the bandgap defect modes in the displacement transmission of the beam. Furthermore, we show that when the beam is excited at the frequency of the defect mode, the flexural waves will be sensitively localized around the crack even inside the band gap and this effect can be used to locate the crack. To experimentally demonstrate the proposed crack identification method, we periodically attach steel balls as concentrated masses on a cracked beam and the crack locating is realized by bonding polyvinylidene fluoride (PVDF) films in a line along the cracked beam segment. Our analytical and experimental results indicate that the phenomenon of the defect modes in imperfect phononic crystals can be applied on crack detection in beams.

中文翻译：

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将带隙缺陷模式应用于使用周期性集中质量的光束裂纹检测

摘要 在本文中，通过应用不完美声子晶体（PCs）带隙中缺陷模式的概念，提出了一种光束裂纹检测方法。在提出的裂纹检测方法中，集中质量的周期性阵列连接在直梁上以产生布拉格带隙。然后，光束中的裂纹可能会在某些带隙中引起缺陷模式，其频率取决于集中质量的周期性或裂纹的位置和大小。使用光谱元素方法公式，我们首先研究集中质量对带隙形成的影响。然后，我们研究了晶格常数或裂纹的大小和位置对梁位移传输中带隙缺陷模式的影响。此外，我们表明，当以缺陷模式的频率激发光束时，即使在带隙内部，弯曲波也会敏感地定位在裂纹周围，这种效应可用于定位裂纹。为了通过实验证明所提出的裂纹识别方法，我们定期将钢球作为集中质量附着在裂纹梁上，并通过沿裂纹梁段将聚偏二氟乙烯 (PVDF) 薄膜粘合成一条线来实现裂纹定位。我们的分析和实验结果表明，不完美声子晶体中的缺陷模式现象可以应用于梁中的裂纹检测。为了通过实验证明所提出的裂纹识别方法，我们定期将钢球作为集中质量附着在裂纹梁上，并通过沿裂纹梁段将聚偏二氟乙烯 (PVDF) 薄膜粘合成一条线来实现裂纹定位。我们的分析和实验结果表明，不完美声子晶体中的缺陷模式现象可以应用于梁中的裂纹检测。为了通过实验证明所提出的裂纹识别方法，我们定期将钢球作为集中质量附着在裂纹梁上，并通过沿裂纹梁段将聚偏二氟乙烯 (PVDF) 薄膜粘合成一条线来实现裂纹定位。我们的分析和实验结果表明，不完美声子晶体中的缺陷模式现象可以应用于梁中的裂纹检测。