Vibration attenuation band tuning by active stiffness control of local resonators of metamaterials

This paper presents a design of metamaterials with a broader bandgap by active stiffness control of local resonators. A series of cantilever beams are connected to the host structure, serving as local resonators to open the bandgap for vibration attenuation. The piezoelectric transducers bonded on the cantilever beams are shunted to a negative capacitance-negative inductance series circuit (NCNL). The variation of the effective modulus of the piezoelectric sample when connected to NCNL is discussed. In addition, the effect of the NC circuit and negative capacitance in series with positive inductance (NC-L) circuit on the effective modulus of shunted piezoelectric transducers is also analyzed for comparison. By tuning the NCNL circuit, the elastic modulus of the beam-type resonator exhibits frequency-dependent, which will achieve active stiffness tuning. Subsequently, the transmittance analysis of a metamaterial beam with active stiffness resonators is conducted using finite element method. The finite element results show that a broader attenuation band can be achieved by properly selecting the parameters of NC-NL circuits. This work provides a promising method for effective vibration attenuation using metamaterials.