单相固体声子晶体的负弹性波折射和聚焦调节

Fei-Yu Liu, Fa-Jie Wang, Sheng-Dong Zhao
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摘要

本文介绍了一种具有规则六边形穿孔图案的单相固体声子晶体(PnC)结构的设计。该结构具有三条负折射带,其中一条用于横波,另两条用于纵波,从而能够同时控制剪切波和纵波。由于三角形晶格的高度对称性,与负折射带相对应的等频曲线接近圆形,这表明负折射效应几乎是各向同性的。这种负折射效应是通过与本文设计的多孔结构密切相关的特定质量共振模式实现的。我们首先分析了 PnC 的带状结构,然后设计了 PnC 板结构,以实现对频率为 32.4 kHz、负折射率为 -1 的横波的负折射控制。此外,在频率为 44 千赫和 64.54 千赫时,还可实现纵波的负折射控制。随后,我们仔细研究了各种条件对负折射的影响,包括不同的结构参数、入射角和工作频率,同时验证了所设计声子晶体结构的稳健性。利用该结构的负折射特性,我们构建了一个弹性波透镜,以实现剪切波和纵波的完美成像。最后,我们利用有限元仿真分析了不同声源位置的聚焦成像特性,验证了结果与理论预期非常吻合。本研究中设计的固体 PnC 结构在弹性波成像领域具有巨大的应用潜力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Negative elastic wave refraction and focusing regulation of single-phase solid phononic crystals
This paper presents the design of a single-phase solid phononic crystal (PnC) structure featuring a regular hexagonal perforation pattern. The structure manifests three negative refraction bands, encompassing one for transverse waves and two for longitudinal waves, thereby enabling simultaneous control of shear and longitudinal waves. Due to the high symmetry of the triangular lattice, the equal frequency curves corresponding to the negative refraction band approach circular shapes, suggesting a nearly isotropic negative refraction effect. This negative refraction effect is achieved through specific mass resonance modes closely related to the porous structure designed in this paper. Initially, we analyze the band structure of the PnC, followed by designing the PnC plate structure to achieve negative refraction control for transverse waves at a frequency of 32.4 kHz, with a negative refraction index of −1. Additionally, negative refraction control for longitudinal waves is attained at frequencies of 44 and 64.54 kHz. Subsequently, we scrutinize the influence of various conditions on negative refraction, including different structural parameters, incident angles, and operating frequencies, while verifying the robustness of the designed phonon crystal structure. Leveraging the negative refraction characteristics of the structure, we construct an elastic wave lens to achieve perfect imaging of shear and longitudinal waves. Finally, employing finite element simulation and analyzing focusing imaging characteristics with different source positions, we validate that the results closely align with theoretical expectations. The solid PnC structure designed in this study holds significant potential for applications in the fields of elastic wave imaging.
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