An adaptive metamaterial beam with hybrid shunting circuits for extremely broadband control of flexural waves

A great deal of research has been devoted to controlling the dynamic behaviors of phononic crystals and metamaterials by directly tuning the frequency regions and/or widths of their inherent band gaps. Here, we report a new class of adaptive metamaterial beams with hybrid shunting circuits to realize super broadband Lamb-wave band gaps at an extreme subwavelength scale. The proposed metamaterial is made of a homogeneous host beam on which tunable local resonators consisting of hybrid shunted piezoelectric stacks with proof masses are attached. The hybrid shunting circuits are composed of negative-capacitance and negative-inductance elements connected in series or in parallel in order to tune the desired frequency-dependent stiffness. It is shown theoretically and numerically that by properly modifying the shunting impedance, the adaptive mechanical mechanism within the tunable resonator can produce high-pass and low-pass wave filtering capabilities for the zeroth-order anti-symmetric Lamb-wave modes. These unique behaviors are due to the hybrid effects from the negative-capacitance and negative-inductance circuit elements. Such a system opens up important perspectives for the development of adaptive vibration or wave-attenuation devices for broadband frequency applications.