弹性中的薄透镜方程:利用梯度指数声子晶体成像

P. H. Beoletto, F. Nistri, A. S. Gliozzi, N. M. Pugno, F. Bosia
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引用次数: 0

摘要

弹性领域的许多研究都借用了光学中的梯度指数透镜(GRIN)概念,用于波的聚焦和控制。这些效应对于隐形、吸收或能量收集应用尤其具有吸引力。在这里,我们采用了另一种 GRIN 透镜设计,它能使输入和输出相位一一对应,并允许使用著名的薄透镜方程确定焦距,从而有效地建立了光学中凸透镜的弹性等效模型。我们用分析方法证明了这一点,获得了点状光源的位置与其图像之间的双射关系,并在铝板上用数值和实验证实了结果,在铝板上,透镜是通过引入直径可变的圆形空腔来实现的。此外,概念验证实验证明了以亚波长分辨率对厘米级挠性波源成像的可能性。这项研究可以将弹性 GRIN 透镜的应用扩展到成像和无损检测等新领域,通过聚焦散射场来确定缺陷位置。多个来源可以同时成像,多个透镜的组合效应还可用于设计更复杂的系统,为弹性波操纵技术的开发开辟了新的可能性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The thin lens equation in elasticity: imaging with gradient index phononic crystals
Many works in elasticity have exploited the concept of gradient index (GRIN) lenses, borrowed from optics, for wave focusing and control. These effects are particularly attractive for cloaking, absorption or energy harvesting applications. Despite their potential, current lens designs suffer from limitations, mainly related to the difficulty in imaging point-like sources. Here, we exploit an alternative GRIN lens design, which enables a one-to-one correspondence between input and output phase, and allows to determine the focal length using the well-known thin lens equation, effectively establishing the elastic equivalent of the convex lens in optics. This is demonstrated analytically, obtaining a bijective relation between the location of a point-like source and its image, and the results are confirmed numerically and experimentally in an aluminium plate, where the lens is realized by introducing rows of circular cavities of variable diameters. Moreover, a proof-of-concept experiment demonstrates the possibility to image sources of flexural waves at the centimetre scale with subwavelength resolution. This research can extend applications of elastic GRIN lenses to new fields such as imaging and non-destructive testing, where the location of defects can be identified by focusing the scattered field. Multiple sources can be imaged simultaneously, and the combined effect of multiple lenses can also be used to design more complex systems, opening new possibilities in the technological exploitation of elastic wave manipulation.
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