Manipulating elastic waves via engineered spatial curvature profiles
Manipulating elastic waves via engineered spatial curvature profiles
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通过工程空间曲率剖面操纵弹性波
DOI：
10.1117/12.2612573
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Ruzzene, Massimo
中科院分区：
文献类型：
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作者：
Mazzotti, Matteo;Gupta, Mohit;Santangelo, Christian;Ruzzene, Massimo
我们研究曲面作为弹性波的测地线透镜。与光学中的发现相一致，我们表明，波的传播发生沿着射线，对应于测地线的曲面，我们建立高斯曲率和折射率之间的几何等价。这种等价性是制定弯曲波在弯曲壳显示，在短波长的限制，射线方程对应于经典方程的测地线。我们利用这个结果来确定一个非欧几里德变换，映射到一个空间变化的平面波导的折射率分布的各向同性弯曲波导的几何轮廓。这些理论预测首先通过数值模拟进行验证，然后通过具有不同曲率分布的3D打印弯曲膜的实验进行验证。数值和实验结果证实，焦区和焦散网络正确预测的基础上测地线评价。我们的研究结果形成的基础上，对应于折射率的空间分布和诱导的焦点，迫使波传播沿着预定义的轨迹弯曲的配置文件的设计。这项研究的结果还表明，曲率作为一个有吸引力的替代战略的基础上，局部剪裁的材料性能和几何图案，已获得普及的梯度折射率透镜设计。
We investigate curved surfaces operating as geodesic lenses for elastic waves. Consistently with findings in optics, we show that wave propagation occurs along rays that correspond to the geodesics of the curved surfaces, and we establish the geometric equivalence between Gaussian curvature and refractive index. This equivalence is formulated for flexural waves in curved shells by showing that, in the short wavelength limit, the ray equation corresponds to the classical equation of geodesics. We leverage this result to identify a non-Euclidean transformation that maps the geometric profile of a isotropic curved waveguide into a spatially varying refractive index distribution for a planar waveguide. These theoretical predictions are validated first through numerical simulations, and subsequently through experiments on 3D printed curved membranes with different curvature distributions. Numerical and experimental findings confirm that focal regions and caustic networks are correctly predicted based on geodesic evaluations. Our results form the basis for the design of curved profiles that correspond to spatial distributions of the refractive index and induce focal points by forcing waves to propagate along predefined trajectories. The findings of this study also suggest curvature as an attractive alternative to strategies based on the local tailoring of material properties and geometrical patterns that have gained in popularity for gradient-index lens design.