CEE Seminar: Elastic Wave Control Through Topology and Curvature
Surface curvature is explored as a largely unexplored route for the design of topological mechanical metamaterials and waveguides. Curvature as a design parameter is first investigated in the context of periodic minimal surfaces, which provide a platform for topological mechanical metamaterials. We specifically illustrate configurations of 1D and 2D lattices dimerized through parametrizations that systematically break spatial symmetries, and that form the bases for opening non-trivial band gaps and for introducing interfaces that support topological valley modes. Their existence is illustrated through vibration and wave propagation experiments conducted on additively manufactured minimal surface samples, which illustrate the confinement of topologically protected edge states along engineered interfaces and confirm the lack of significant backscattering at sharp corners. This study supports the vision of minimal surfaces as a general framework where geometrical modulations and symmetries can be introduced to achieve novel and unusual mechanical and acoustic functionalities.
In the second part of the talk, curvature is explored as a mean to induce spatial variations of the effective refractive index of waveguides. Graded refractive index distributions usually requires the use of metamaterials, which pose manufacturing challenges, and introduce bandwidth limitations. It is here shown that the effect of a variable refractive index is equivalently achieved by warping the waveguide in space. We specifically illustrate how elastic waves can be manipulated through curved surfaces characterized by generic Gaussian curvature distributions. By operating within the short wavelength limit, we show that homogeneous curved waveguides can be designed by relating the refractive index to the Gaussian curvature. Consequently, the wave trajectories can be predicted by means of geodesic analysis of the surface followed by a classical ray tracing approach. Our theoretical predictions are validated by experiments conducted on additively printed curved waveguides which demonstrate how spatial curvature can be used for wave guiding and focusing using simple, and possible reconfigurable, structural configurations.