A periodic array of resistive inductive (RL) shunted piezoelectric (PZT) patches is applied to achieve tunable low-frequency locally resonant (LR) band gaps in a flexible isotropic beam. Each pair of surface-bonded PZT patches is linked to an independent RL circuit. All the circuits are the same and are tuned synchronously. A transfer matrix methodology is used to calculate the frequency range and attenuation properties of the LR band gap. Two main differences are found between the LR band gaps induced by shunting circuits and traditional oscillators. Antoniou's circuits are used to produce large ideal inductances necessary for low eigenfrequencies. The theoretical results are experimentally validated by measuring the harmonic response of the beam. Significant attenuation in the low-frequency LR band gap is observed.
Periodic arrays of piezoelectric patches connected by enhanced resonant shunting circuits are attached to a slender beam to control the propagation of vibration. Numerical models based on the transfer matrix methodology are constructed to predict the band structure, attenuation factors and the transmission of vibration in the proposed smart structure. The vibration attenuations of the proposed smart structure and that with the passive resonant shunting circuits are compared in order to verify the efficiency of the enhanced resonant shunting circuits. Vibration experiments are conducted in order to validate the theoretical predictions. The specimen with a combination of different types of resonant shunting circuits is also studied in order to gain wider attenuation frequency ranges.
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.
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