Active metamaterials with broadband controllable stiffness for tunable band gaps and non-reciprocal wave propagation

One dimensional active metamaterials with broadband controllable bending stiffness are studied in this paper. The key unit of the active metamaterials is composed of a host beam and piezoelectric patches bonded on the beam surfaces. These patches serve as sensors or actuators. An appropriate feedback control law is proposed in order to change the bending stiffness of the active unit. The input of the control law is the voltage on the sensors, the output is the voltage applied on the actuators. Due to the control, bending stiffness of the active unit is (1 + alpha) times of that of the bare host beam, alpha being a design parameter in the control law. The bending stiffness can be tuned to desired value by changing alpha. The performances of the controlled bending stiffness are analytically and numerically studied, the stability issues are also discussed. The active units are first used in a spatial periodic waveguide to have tunable band gaps, then they are integrated in a spatiotemporal periodic waveguide to realize non-reciprocal wave propagation. Performances of the two waveguides are numerically studied.