Structural periodicity dependent scattering behavior in parity-time symmetric elastic metamaterials

We investigate the effect of structural periodicity on elastic longitudinal and flexural wave propagation in parity-time ($\mathcal{PT}$) symmetric prototypical elastic metamaterial rods and beams. Through theoretical analysis and numerical demonstration, we reveal the link between the observed band structure of infinite periodic $\mathcal{PT}$ symmetric elastic metamaterials and the unique scattering properties of the corresponding finite periodic $\mathcal{PT}$ symmetric systems. In particular, we study the coherent perfect absorber and laser (CPAL). There is an observed periodic-like occurrence of the CPAL formation when varying the cell number in the finite periodic metamaterial that correlates to the band structure of the infinite periodic system. For this, we provide simple equations to estimate the periodicity and the minimum cell number. Using a piezoelectric-aided elastic metamaterial consisting of piezoelectric patches and active circuits, we propose a feasible configuration to realize tunable flexural wave CPALs in a periodic-structured $\mathcal{PT}$ symmetric metamaterial beam, and demonstrate that the CPAL can be induced in the Bragg's bandgap.