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Flexural wave band gaps in metamaterial beams with membrane-type resonators: theory and experiment

This paper deals with flexural wave band gaps in metamaterial beams with membrane-type resonators. The proposed membrane-type resonator consists of a tensioned elastic membrane and a mass block attached to the center of the membrane. Numerical models based on finite element method are presented to predict the dispersion relation, band gaps and eigen-modes. It has shown that the metamaterial beams exhibit unique wave physics. A broad Bragg band gap (BBG) and two low-frequency locally resonant band gaps (LRBGs) can be observed due to the structural periodicity and locally resonant behavior respectively. The first LRBG can be ascribed to the combined resonance of the membranes and the masses, while the second LRBG is caused by the resonance of the membranes. The study of the effective property shows that negative mass density occurs in the LRBGs. The effects of membrane tension and mass magnitude (the weight of mass block) on the LRBGs are further analyzed. It is shown that both the two LRBGs move to high-frequency with the increase of the membrane tension. However, as the mass magnitude increases, the first LRBG moves to low-frequency and the second LRBG almost remains unchanged. It is further demonstrated that, when a larger unit cell with multiple kinds of masses (a larger unit cell incorporating multiple basic unit cells but with different weights of mass blocks within each basic unit cell) are used, the first LRBG can be broadened, which can be employed to achieve broadband vibration attenuation. Moreover, experimental measurements of vibration transmittance are conducted to validate the theoretical predictions. Good agreements between the experimental results and the theoretical predictions are observed.