Cui Hanyin, Lin Weijun, Zhang Hailan, Wang Xiuming, Trevelyan Jon
State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
School of Engineering and Computing Sciences, Durham University, Durham DH1 3LE, United Kingdom.
J Acoust Soc Am. 2014 Jun;135(6):3398-408. doi: 10.1121/1.4872297.
It is known that modes in axially uniform waveguides exhibit backward-propagation characteristics for which group and phase velocities have opposite signs. For elastic plates, group velocities of backward Lamb waves depend only on Poisson's ratio. This paper explores ways to achieve a large group velocity of a backward mode in hollow cylinders by changing the outer to inner radius ratio, in order that such a mode with strong backward-propagation characteristics may be used in acoustic logging tools. Dispersion spectra of guided waves in hollow cylinders of varying radii are numerically simulated to explore the existence of backward modes and to choose the clearly visible backward modes with high group velocities. Analyses of group velocity characteristics show that only a small number of low order backward modes are suitable for practical use, and the radius ratio to reach the highest group velocity corresponds to the accidental degeneracy of neighboring pure transverse and compressional modes at the wavenumber k = 0. It is also shown that large group velocities of backward waves are achievable in hollow cylinders made of commonly encountered materials, which may bring cost benefits when using acoustic devices which take advantage of backward-propagation effects.
众所周知，轴向均匀波导中的模式具有反向传播特性，其群速度和相速度符号相反。对于弹性板，反向兰姆波的群速度仅取决于泊松比。本文探讨了通过改变外径与内径之比来实现空心圆柱中反向模式的大群速度的方法，以便这种具有强反向传播特性的模式可用于声波测井工具。对不同半径空心圆柱中导波的色散谱进行了数值模拟，以探索反向模式的存在，并选择具有高群速度且清晰可见的反向模式。群速度特性分析表明，只有少数低阶反向模式适合实际应用，达到最高群速度的半径比对应于波数k = 0时相邻纯横向模式和压缩模式的偶然简并。研究还表明，在常用材料制成的空心圆柱中可以实现反向波的大群速度，这在使用利用反向传播效应的声学装置时可能会带来成本效益。
