Large low-frequency vibration attenuation induced by arrays of piezoelectric patches shunted with amplifier–resonator feedback circuits

Periodic arrays of piezoelectric patches shunted by amplifier–resonator circuits are attached to a beam in order to gain large low-frequency attenuations in the propagation of flexural beam vibration. A numerical model based on the transfer matrix methodology and Bloch theory are built to predict the band gaps and attenuation factors as well as the transmission of vibration in the proposed smart metamaterials. Influences of circuital parameters on attenuation factors and the equivalent Young's modulus are studied. It is found that the central frequency of attenuations is lower than the resonant frequency because of the negative equivalent elastic modulus of piezoelectric patches at frequencies lower than the resonance. Finite element simulations and vibration experiments are conducted on a 10 mm-thick aluminium alloy beam with six pairs of piezoelectric patches glued on it. Based on theoretical calculations, three sets of circuital parameters are chosen to gain large vibration transmission attenuations around the lowest three modal peaks. Significant attenuation is found in the experimental results, which is predicted in theoretical calculations and finite element simulations. A superlattice metamaterial specimen with a combination of three different sets of circuital parameters is also studied in order to gain wide attenuation frequency ranges.