We derive the elastic properties of a cylindrical cloak for in-plane coupled shear and pressure waves. The cloak is characterized by a rank 4 elasticity tensor with spatially varying entries, which are deduced from a geometric transform. Remarkably, the Navier equations retain their form under this transform, which is generally untrue [G. W. Milton et al., N. J. Phys. 8, 248 (2006)]. The validity of our approach is confirmed by comparison of the analytic Green’s function in homogeneous isotropic elastic space against full-wave finite element computations in a heterogeneous anisotropic elastic region surrounded by perfectly matched layers.

We propose a type of locally resonant structure involving arrays of structured coated inclusions. The coating consists of a structural interface with beams inclined at a certain angle. Such an elastic metamaterial supports tunable low-frequency stop bands associated with localized rotational modes that can be used in the design of filtering, reflecting, and focusing devices. Asymptotic estimates for resonant frequencies are in good agreement with finite element computations and can be used as a design tool to tune stop band changing relative inclinations, number, and cross section of the beams. Inertial resonators with inclined ligaments allow for anomalous dispersion (negative group velocity) to occur in the pressure acoustic band and this leads to the physics of negative refraction, whereby a point force located above a finite array of resonators is imaged underneath for a given polarization. We finally observe that for a periodic macrocell of the former inertial resonators with one defect in the middle, an elastic trapped mode exists within a high-frequency stop band. The latter design could be used in the enhancement of light and sound interactions in photonic crystal fiber preforms.