Experiments on Maxwell's fish-eye dynamics in elastic plates

Abstract

We experimentally demonstrate that a Duraluminium thin plate with a thickness profile varying radially in a piecewise constant fashion as h(r) = h(0)(1 + (r/Rmax)2 ) 2 , with h(0) = 0.5 mm, h(Rmax) = 2 mm and Rmax = 10 cm behaves in many ways as Maxwell's fish-eye lens in optics, since its imaging properties for a Gaussian pulse with central frequencies 30 kHz and 60 kHz are very similar to those predicted by ray trajectories (great circles) on a virtual sphere (rays emanating from the North pole meet at the South pole). However, refocusing time depends on the carrier frequency as a direct consequence of the dispersive nature of flexural waves in thin plates. Importantly, experimental results are in good agreement with FiniteDifference-Time-Domain simulations.

Pulse Dynamics of Flexural Waves in Transformed Plates

“…This approach has been validated for adiabatically varying thickness, for example, for the design of elastic lenses. [ 49–51 ] Here, we demonstrate that, in contrast to an adiabatically varying thickness, a periodic change of plate thickness on a subwavelength scale can be utilized to design effective anisotropic metamaterials for flexural waves. A significant advantage in terms of realization is that a single material is required and that the subwavelength structuration is easily implemented by surface machining or, more conveniently, by 3D printing, a technique now readily available for many types of materials, including ceramics and metals.…”

“…Keeping all elastic parameters constant, the rigidity for each layer, D a and D b , is easily implemented by adjusting the thickness, h a and h b , of the plate at each layer, following the definition of D . [ 21,49–51 ] According to Equation (5), the thickness difference h a − h b increases steeply for θ above 40° (see Figure S1, Supporting Information). We therefore choose for the experimental realization an angle θ = 20°, in order to limit the geometrical constraints for the 3D‐printing.…”

Maxwell Fisheye Lens Based Retrodirective Array

“…Generally, one can implement a variety of technologies in order to create a refractive index profile that performs fisheye focusing e.g. thin plates 4 , holy parallel plates 5 . In this paper we take a different approach in which fisheye principle is realized using the mode theory of a parallel-plate waveguide 6 .…”

Comparison of Lamb wave focusing performance using wave dispersion-compensated actuation and plano-concave lenses

“…This method is referred to as focusing and allows users to generate high-amplitude signals at the "hot spot," thus improving the signal-to-noise ratio in pitch-catch and pulse-echo methods used for damage quantification. Lamb wave mode focusing can be achieved using gradient-index phononic crystals [2][3][4][5][6][7] or locally resonant metamaterials, [8][9][10] phased-array beamforming, [11][12][13][14] dispersion-compensated actuation, 15 and plano-concave slice lenses. 16 Wu et al numerically demonstrated focusing of the A0 mode of Lamb waves in a gradient-index phononic crystal.…”

“…20 Lefebvre et al performed experiments on a thin aluminum plate with a thickness profile that varied radially in order to cause an effect resembling that of Maxwell's fish-eye lenses in optics. 7 They studied the imaging properties of this plate using a Gaussian pulse with central frequencies of 30 kHz and 60 kHz. They concluded that the refocusing time depends on the carrier frequency as a direct consequence of the dispersive nature of flexural waves in thin plates.…”