S_0兰姆波在渐变折射率声透镜中的聚焦

Focusing of the Lowest-Order Symmetric Lamb Wave in Gradient-Index Phononic Crystal Plate

本文研究了S_0兰姆波在渐变折射率声子晶体中的聚焦现象.通过调整正方晶格声子晶体的主轴方向与波传播的相对方向,设计了ΓX和ΓM方向两组不同的渐变折射率声透镜.采用有限单元法模拟S_0波在不同声透镜内的传播,并与S_0波在声透镜内的传播迹线做了对比,数值结果和理论结果基本一致.数值计算结果显示:ΓX方向的声透镜的焦距fl略大于其理论值,而ΓM方向的声透镜的fl则略小于其理论值.ΓX方向的声透镜的横向分辨率FWHM小于ΓM方向的声透镜,而聚焦强度MFI则大于ΓM方向的声透镜.结果表明,通过调整声子晶体的主轴方向与波传播的相对方向,可以显著地改变声透镜的聚焦特征.这为S_0兰姆波声透镜的设计提供了重要依据.

In this work, the focalization of the lowest-order Lamb （So） wave in the gradient-index phononie crystal plate or acoustic lens was investigated. Two kinds of acoustic lenses, namely ГX or FM lenses respectively, were designed by adjusting the principal orientations ГX or FM of phononic crystals relative to the propagation direction of incident waves. The numerical results obtained by the finite element method show good agreement with the theoretical results represented by the ray trajectories of So mode in the lenses computed by the geometrical formalism. It shows that the FX lens leads to a focal distance larger than its theoretical value while the FM lens leads to the contrary. Furthermore, the FX lens has a full width at half maximum （FWHM） smaller than the FM lens, and a maximum field intensity （MFI） larger than its ГM counterpart. Both the numerical and theoretical results show that adjusting the principal orientation can effectively affect the characteristics of the focalization of So wave, which provides useful suggestions for designing future acoustic lenses.