A major obstacle in designing a perfect cloak for objects in shallow-water waves is that the linear transformation media scheme (also known as transformation optics) requires spatial variations of two independent medium properties. In the Maxwell's equation and for the well-studied problem of electromagnetic cloaking, these two properties are permittivity and permeability. Designing an anisotropic material with both variable permittivity and variable permeability, while challenging, is achievable. On the other hand, for long gravity waves, whose governing equation maps one-to-one to the single polarization Maxwell's equations, the two required spatially variable properties are the water depth and the gravitational acceleration; in this case changing the gravitational acceleration is simply impossible. Here we present a nonlinear transformation that only requires the change in one of the medium properties, which, in the case of shallow-water waves, is the water depth, while keeping the gravitational acceleration constant. This transformation keeps the governing equation perfectly intact and, if the cloak is large enough, asymptotically satisfies the necessary boundary conditions. We show that with this nonlinear transformation an object can be cloaked from any wave that merely satisfies the long-wave assumption. The presented transformation can be applied as well for the design of non-magnetic optical cloaks for electromagnetic waves.
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.
Materials with target nonlinear mechanical response can support the design of innovative soft robots, wearable devices, footwear, and energy‐absorbing systems, yet it is challenging to realize them. Here, mechanical metamaterials based on hinged quadrilaterals are used as a platform to realize target nonlinear mechanical responses. It is first shown that by changing the shape of the quadrilaterals, the amount of internal rotations induced by the applied compression can be tuned, and a wide range of mechanical responses is achieved. Next, a neural network is introduced that provides a computationally inexpensive relationship between the parameters describing the geometry and the corresponding stress–strain response. Finally, it is shown that by combining the neural network with an evolution strategy, one can efficiently identify geometries resulting in a wide range of target nonlinear mechanical responses and design optimized energy‐absorbing systems, soft robots, and morphing structures.
Transition waves that sequentially switch bistable elements from one stable configuration to another have received significant interest in recent years not only because of their rich physics but also, for their potential applications, including unidirectional propagation, energy harvesting, and mechanical computation. Here, we exploit the propagation of transition waves in a bistable one-dimensional (1D) linkage as a robust mechanism to realize structures that can be quickly deployed. We first use a combination of experiments and analyses to show that, if the bistable joints are properly designed, transition waves can propagate throughout the entire structure and transform the initial straight configuration into a curved one. We then demonstrate that such bistable linkages can be used as building blocks to realize deployable three-dimensional (3D) structures of arbitrary shape.
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