板中Lamb波与管中纵向模态的传播特性的对比分析
Comparison Analysis of the Propagation Characteristics of Lamb Waves in Plates and Longitudinal Waves in Pipes
摘 要
从Navier运动方程出发，根据不同波导的结构和边界条件，分别推导了平板中Lamb波和管道中纵向模态导波的特征方程，并求解了它们的频散关系和模态结构。通过对平板中Lamb波与管道中纵向模态的特征方程的对比分析，发现了如果管道和平板的材料和壁厚都一致，且当管道半径足够大时，管道中纵向模态的特征方程可化简为平板中Lamb波的特征方程。通过比较频散曲线，得出以下结论：随着管道内径增加，管道中纵向模态的频散关系逐渐趋近于平板中Lamb波的频散关系：其中，管道中的纵向模态L（0，1）趋近于平板中的A0模态：管道中的纵向模态L（0，2）趋近于平板中的S0模态。
纵向模态
频散曲线
模态结构
Lamb wave
Longitudinal mode
Dispersion curve
Mode shape
Abstract
This paper derives the characteristic equations, dispersion curves and mode shapes of Lamb waves in plates and longitudinal mode guided waves in pipes in details by solving the Navier equation for different waveguide structures and boundary conditions. By comparing the characteristic equations of Lamb waves and longitudinal mode guided waves, it can be found that for pipes and plates that have the same material and wall thickness, the characteristic equations of longitudinal modes in pipes can be simplified to the characteristic equations of Lamb waves in plates when the pipe radius is large enough. Moreover, through the comparison of dispersion curves, it has been found that the dispersion relations of pipes gradually approach to the dispersion relations of plates. Particularly, the longitudinal mode L (0, 1) in pipes approaches to the A0 mode in plates, and the longitudinal mode L (0, 2) in pipes approaches to the S0 mode in plates.
中图分类号 TB559 TG115.28 DOI 10.11973/wsjc201704009
所属栏目 试验研究
基金项目 国家自然科学基金资助项目（51134016）；中央高校基本科研业务专项资金资助项目（2016XS25）
收稿日期 2016/11/2
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备注郭鹏(1986-),男,博士研究生,研究方向为电站设备状态监测、结构健康监测和超声无损检测技术。
引用该论文: GUO Peng,TIAN Zhen-hua,LI Hong-yuan,XU Hong. Comparison Analysis of the Propagation Characteristics of Lamb Waves in Plates and Longitudinal Waves in Pipes[J]. Nondestructive Testing, 2017, 39(4): 42～48
郭鹏,田振华,李鸿源,徐鸿. 板中Lamb波与管中纵向模态的传播特性的对比分析[J]. 无损检测, 2017, 39(4): 42～48
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参考文献
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【2】ROSE J L. Ultrasonic waves in solid media[M]. UK: Cambridge University Press, 2004.
【3】邢耀淇, 高佳楠, 陈以方. 超声近场导波在薄壁管检测中的应用[J]. 无损检测, 2016, 38(2): 5-8.
【4】吴斌, 曹海洋, 刘秀成, 等. 干耦合式磁致伸缩导波管道检测系统[J]. 无损检测, 2016, 38(9): 9-13.
【5】刘胜, 骆苏军. 基于超声导波技术的长输管道无损检测[J]. 无损检测, 2015, 37(6): 1-3.
【6】THOMSON W T. Transmission of elastic waves through a stratified solid medium[J]. Journal of Applied Physics, 1950, 21(2): 89-93.
【7】HASKELL N A. The dispersion of surface waves on multilayered media[J]. Bulletin of the Seismological Society of America, 1953, 43(1): 17-34.
【8】LOWE M J S. Matrix techniques for modeling ultrasonic waves in multilayered media[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 1995, 42(4): 525-542.
【9】何存富, 刘青青, 焦敬品, 等. 基于振动模态分析的钢轨中超声导波传播特性数值计算方法[J]. 振动与冲击, 2014, 33(3): 9-13.
【10】BARTOLI I, MARZANI A, DI SCALEA F L,et al. Modeling wave propagation in damped waveguides of arbitrary cross-section[J]. Journal of Sound and Vibration, 2006, 295(3): 685-707.
【11】ELMAIMOUNI L, LEFEBVRE J E, ZHANG V, et al. A polynomial approach to the analysis of guided waves in anisotropic cylinders of infinite length[J]. Wave Motion, 2005, 42(2): 177-189.
【12】GRAVENKAMP H, SONG C, PRAGER J. A numerical approach for the computation of dispersion relations for plate structures using the scaled boundary finite element method[J]. Journal of Sound and Vibration, 2012, 331(11): 2543-2557.
【13】田振华, 徐鸿, 杨志磊. 基于扭转模态的管道裂纹聚焦成像[J]. 中国机械工程, 2013, 24(1): 85-89.
【14】田振华, 徐鸿, 李鸿源, 等. 基于单激发端多接收端压电阵列的板内损伤检测[J]. 中国机械工程, 2014, 25(22): 3077-3080, 3087.
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