A hybrid elastic metamaterial with negative mass density and tunable bending stiffness

Achieving vibration and/or wave attenuation with locally resonant metamaterials has attracted a great deal of attention due to their frequency dependent negative effective mass density. Moreover, adaptive phononic crystals with shunted piezoelectric patches have also demonstrated a tunable wave attenuation mechanism by controlling electric circuits to achieve a negative effective stiffness. In this paper, we propose an adaptive hybrid metamaterial that possesses both a negative mass density as well as an extremely tunable stiffness by properly utilizing both the mechanical and electric elements. A multi-physical analytical model is first developed to investigate and reveal the tunable wave manipulation abilities in terms of both the effective negative mass density and/or bending stiffness of the hybrid metamaterial. The programmed flexural wave manipulations, broadband negative refraction and waveguiding are then illustrated through three-dimensional (3D) multi-physical numerical simulations in hybrid metamaterial plates. Our numerical results demonstrate that the flexural wave propagation can essentially be switched between “ON/OFF” states by connecting different shunting circuits.