Abstract
Conical refraction, which is quite well-known in electromagnetic waves, has not been explored well in elastic waves due to the lack of proper natural elastic media. Here, we propose and design a unique anisotropic elastic metamaterial slab that realizes conical refraction for horizontally incident longitudinal or transverse waves; the single-mode wave is split into two oblique coupled longitudinal-shear waves. As an interesting application, we carried out an experiment of parallel translation of an incident elastic wave system through the anisotropic metamaterial slab. The parallel translation can be useful for ultrasonic non-destructive testing of a system hidden by obstacles. While the parallel translation resembles light refraction through a parallel plate without angle deviation between entry and exit beams, this wave behavior cannot be achieved without the engineered metamaterial because an elastic wave incident upon a dissimilar medium is always split at different refraction angles into two different modes, longitudinal and shear.
Highlights
The wave behavior in an anisotropic medium can be quite different from that in an isotropic medium
As reported earlier[5], conical refraction for elastic waves occurs if C11 = C66 and C16 = C26 = 0 where Cij denotes the component of the stiffness tensor C
Because the phase speeds of longitudinal and transverse waves are given by VL = C11/ρ and VT = C66/ρ (ρ: density), respectively, the relation of C11 = C66 implies that VL should be equal to VT
Summary
The wave behavior in an anisotropic medium can be quite different from that in an isotropic medium. It will be shown that two phase-tuned elastic waves of different modes, longitudinal and transverse (i.e., shear) modes, must be simultaneously transmitted into the metamaterial to achieve the wave translation depicted in the right illustration of Fig. 1a. Since an elastic wave incident upon a dissimilar medium in a plane is always split into two different modes, longitudinal and transverse, at different refraction angles, the parallel translation of waves in the elastic field is different from that in the electromagnetic field. The unit cell of the metamaterial is so designed that it retards its longitudinal speed more than its shear wave speed relative to the wave speeds in the base aluminum plate
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