Comparison Analysis of the Propagation Characteristics of Lamb Waves in Plates and Longitudinal Waves in Pipes
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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。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.
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Keywords:
- Lamb wave /
- Longitudinal mode /
- Dispersion curve /
- Mode shape
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