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

Abstract: 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. Giving thanks to the introduced digital control technique, shunting strategies with transfer functions that can hardly be realized with analog circuits is possible now. 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 the normalized frequency as low as 0.077) are achieved. The underlying physical mechanism is attributed to the negative group velocity of flexural wave within bandgaps. As digital controllers can be readily adapted via wireless broadcasting, the bandgaps can be tuned easily instead of tuning the electric components in analog shunting circuits one by one manually. The theoretical results are well verified experimentally with the measured vibration transmission properties where large insulations of up to 20dB in low-frequency ranges are observed.