Continuous profile flexural GRIN lens: Focusing and harvesting flexural waves

摘要

A significant challenge in flexural wave energy harvesting is the design of an aberration-free lens capable of finely focusing waves over a broad frequency range. To date, flexural lenses have been created using discrete inclusions, voids, or stubs, often in a periodic arrangement, to focus waves via scattering. These structures are narrowband either because scattering is efficient over a small frequency range or the arrangements exploit Bragg scattering bandgaps, which themselves are narrowband. In addition, current lens designs are based on a single frequency and approximate the necessary refractive index profile discretely, introducing aberrations and frequency-dependent focal points. Here, we design a flexural GRIN lens in a thin plate by smoothly varying the plate's rigidity and thus its refractive index. Our lens (i) is broadband since the design does not depend on frequency and does not require bandgaps, (ii) has a fixed focal point over a wide range of frequencies, and (iii) is theoretically capable of zero-aberration focusing. We numerically explore our Continuous Profile GRIN lens (CP-GRIN lens) and then experimentally validate an implemented design. Furthermore, we use a piezoelectric energy harvester disk, located at the first focus of the CP-GRIN, to document improvements in power gain.