Flexural wave band-gaps in phononic metamaterial beam with hybrid shunting circuits

Periodic arrays of hybrid-shunted piezoelectric patches are used to control the band-gaps of phononic metamaterial beams. Passive resistive-inductive (RL) shunting circuits can produce a narrow resonant band-gap (RG), and active negative capacitive (NC) shunting circuits can broaden the Bragg band-gaps (BGs). In this article, active NC shunting circuits and passive resonant RL shunting circuits are connected to the same piezoelectric patches in parallel, which are usually called hybrid shunting circuits, to control the location and the extent of the band-gaps. A super-wide coupled band-gap is generated when the coupling between RG and the BG occurs. The attenuation constant of the infinite periodic structure is predicted by the transfer matrix method, which is compared with the vibration transmittance of a finite periodic structure calculated by the finite element method. Numerical results show that the hybrid-shunting circuits can make the band-gaps wider by appropriately selecting the inductances, negative capacitances, and resistances.