Wu Wenjun, Dong Hao, Zhang Shangyu
School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan, 430063, China.
Sci Rep. 2022 Jul 21;12(1):12488. doi: 10.1038/s41598-022-16708-z.
The scattering of guided waves propagating through pipe bends is studied by means of normal mode expansion. First, the bi-orthogonality relationship for normal modes in pipe bends is derived, based on which the displacement and stress fields at the interfaces between the straight and curved parts are expanded with the normal modes in both parts. Then, based on the displacement and stress field continuity principle, the scattering problem is regarded as an eigenproblem of a transfer matrix, the solution of which gives the mode conversions at the interfaces. A case study is presented of the low-frequency longitudinal mode incident on a pipe bend, and it is found that the dominant mode conversions are L(0,1) reflection and mode conversion from L(0,1) to F(1,1). Finite element simulations and experiments are also conducted. L(0,1) bend reflection and mode-converted F(1,1) are clearly observed, which agrees well with the theoretical predictions.
采用简正模展开法研究了导波在管道弯头中的散射特性。首先，推导了管道弯头中简正模的双正交关系，在此基础上，用直管段和弯管段的简正模对直管段与弯管段界面处的位移场和应力场进行展开。然后，基于位移场和应力场的连续原理，将散射问题归结为一个传递矩阵的本征值问题，求解该本征值问题可得到界面处的模式转换情况。给出了低频纵向模态入射到管道弯头的实例研究，结果表明，主要的模式转换为L(0,1)反射以及从L(0,1)到F(1,1)的模式转换。还进行了有限元模拟和实验。清晰地观察到了L(0,1)弯头反射和模式转换后的F(1,1)，这与理论预测结果吻合良好。
