Multi-resonant piezoelectric shunting induced by digital controllers for subwavelength elastic wave attenuation in smart metamaterial

Instead of analog electronic circuits and components, digital controllers that are capable of active multi-resonant piezoelectric shunting are applied to elastic metamaterials integrated with piezoelectric patches. Thanks to recently introduced digital control techniques, shunting strategies are possible now with transfer functions that can hardly be realized with analog circuits. As an example, the `pole-zero' method is developed to design single-or multi-resonant bandgaps by adjusting poles and zeros in the transfer function of piezoelectric shunting directly. Large simultaneous attenuations in up to three frequency bands at deep subwavelength scale (with normalized frequency as low as 0.077) are achieved. The underlying physical mechanism is attributable to the negative group velocity of the flexural wave within bandgaps. As digital controllers can be readily adapted via wireless broadcasting, the bandgaps can be tuned easily unlike the electric components in analog shunting circuits, which must be tuned one by one manually. The theoretical results are verified experimentally with the measured vibration transmission properties, where large insulations of up to 20 dB in low-frequency ranges are observed.