弯曲波-纵波彩虹捕获效应及其模式转换

Rainbow Trapping of Flexural-Longitudinal Wave and Its Mode Conversion

摘要:

弹性波彩虹捕获效应是指不同频率成分的弹性波在结构的不同位置停止向前传播并发生能量聚集的现象，而弹性波模式转换是指弹性波在传播的过程中其极化方向发生改变的现象。利用彩虹捕获效应实现弹性波模式转换是弹性波操控领域一个新的方向。为了实现弯曲波和纵波之间的双向模式转换，提出了一种梯度结构梁。通过传递矩阵法解析求解了子胞的能带结构，利用有限元法验证了其正确性。根据子胞的能带结构，从波数演化角度解释了弯曲波-纵波彩虹捕获效应及其模式转换的产生机理。通过有限元仿真，验证了弯曲波-纵波彩虹捕获效应以及彩虹捕获效应发生时弯曲波和纵波的双向模式转换。

Abstract:

When broadband elastic waves propagate in a graded structure， the waves of different frequency components will stop propagating forward and have energy accumulation at different positions of the structure， which is called elastic wave rainbow trapping. Mode conversion refers to the phenomenon in which the polarization of elastic waves changes during propagation. The use of rainbow trapping to achieve mode conversion of elastic waves is an emerging research direction in the field of wave manipulation. In order to achieve bidirectional mode conversion of flexural wave and longitudinal wave through rainbow trapping， a beam with graded pillars is proposed in this paper. The band structures of the subunits are solved by adopting the transfer matrix method， and their correctness is verified by using the finite element method. According to the band structures of the subunits， the mechanism of the flexural-longitudinal wave rainbow trapping and its mode conversion is explained from the perspective of wave number change. The flexural-longitudinal wave rainbow trapping is verified by finite element frequency domain simulation. The bidirectional mode conversion of flexural wave and longitudinal wave when flexural-longitudinal wave rainbow trapping occurs is verified by finite element time domain simulation.