Dynamics of an elastic chiral lattice: polarization and shielding properties
Michele Brun (Università di Cagliari), Alexander Movchan (University of Liverpool), Iéan Jones (Liverpool John Moores University)
Mechanics and Dynamics of Periodic Structures
Wed 1:30 - 2:50
Salomon 101
We consider a two-dimensional elastic lattice with an embedded system of spinners [1]. The elastic metamaterial structure possesses cloaking properties owing to built-in micro-rotations. The expression for the ‘chiral term’ in the equations describing the dynamics of the lattice is derived from analysis of the motion of the spinners. The dispersion properties of the structure are analyzed and novel properties of Bloch waves in discrete vortex-type elastic lattices have been identified. Critical regimes have been detected above which waves are polarized only to shear type and pressure type waves cannot propagate. Numerical examples are given in the long wave continuum approximation model, where it is shown that the chiral metamaterial can be used to design a composite cloak around an inclusion, so that the incident waves are guided around the inclusion. The interaction between the incident wave, the structured cloak and the inclusion can lead to a substantial reduction of the shaded region behind the dishomogeneity and to the observation that the coating can be interpreted as a polarizing cloak. The parameters of the chiral coating can also be tuned so that the shaded region is enhanced and the amplitude of the displacement behind the inclusion becomes negligibly small. Applications in the fields of geophysics and structural design of cloaks shielding defects, which interact with elastic waves, are envisaged.