Transverse waves in a dispersive metamaterial with spherical inclusions

The propagation of transverse waves in a dispersive composite with solid inclusions is considered as propagation in a pseudoinhomogeneous medium whose effective properties, namely, the dynamic density and the shear rotational elasticity, depend in a resonance way on the wave frequency and the parameters of translatory and rotary oscillations of inclusions. Estimates are obtained for the natural oscillation frequencies of spherical inclusions in an incompressible elastic medium and for other internal dynamic parameters of the composite that determine the frequency bands corresponding to negative values of the dynamic density and the shear rotational elasticity. When the dynamic properties are simultaneously negative, the dispersive composite is an acoustic metamaterial, which, from the viewpoint of certain specific effects, is analogous to left-handed electrodynamic media much discussed in the literature. The parameters of the composite and the transverse wave frequencies at which the metamaterial properties can be achieved in practice are estimated.