Manipulating elastic waves via engineered spatial curvature profiles

Matteo Mazzotti; Mohit Gupta; Christian Santangelo; Massimo Ruzzene

doi:10.1117/12.2612573

19 April 2022 Manipulating elastic waves via engineered spatial curvature profiles

Matteo Mazzotti, Mohit Gupta, Christian Santangelo, Massimo Ruzzene

Proceedings Volume 12048, Health Monitoring of Structural and Biological Systems XVI; 1204804 (2022) https://doi.org/10.1117/12.2612573
Event: SPIE Smart Structures + Nondestructive Evaluation, 2022, Long Beach, California, United States

Abstract

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.

Conference Presentation

Citation Download Citation

Matteo Mazzotti, Mohit Gupta, Christian Santangelo, and Massimo Ruzzene "Manipulating elastic waves via engineered spatial curvature profiles", Proc. SPIE 12048, Health Monitoring of Structural and Biological Systems XVI, 1204804 (19 April 2022); https://doi.org/10.1117/12.2612573

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