Digital controlled nonlinear smart metamaterial for broadband elastic wave attenuation

One challenge for traditional elastic metamaterials involves broadening the low-frequency bandgap width. To this end, this study presents a new design of a bi-nonlinear smart metamaterial (BNSM) consisting of a host beam and periodically bonded piezoelectric patches with soft and hard nonlinear shunting circuits. A nonlinear finite element model is developed accounting for both piezoelectric coupling effects and electrical nonlinear dynamics to predict the attenuation constants and wave transmissions in the proposed smart metamaterial. Experimental tests are conducted to validate the theoretical predictions. Theoretical and experimental results show that the proposed BNSM can achieve excellent vibration attenuation in low-frequency range. By alternating soft and hard nonlinear shunting circuits, a soft or hard nonlinear local resonance bandgap (NLRB) is generated, respectively, where the soft NLRB extends to higher frequencies, the hard NLRB does vice versa, and each NLRB exhibits attenuation characteristic over a wider frequency range compared to the locally resonant (LR) bandgap. When both NLRBs are activated simultaneously, a broad Bi-NLRB bandgap exceeding 200 Hz is formed, which is 1.7 (1.6) times wider than single hard (soft) NLRB, even 3.9 times wider than the LR bandgap. Moreover, within the majority of the frequency range of each NLRB, the equivalent elastic modulus values are negative. This study introduces a method to fabricate smart nonlinear metamaterials and offers promise for wide-frequency vibration control on flexible structures.