Active tuning of the vibration and wave propagation properties in electromechanical metamaterial beam

Locally resonant metamaterial beams made from flexible substrates with piezoelectric layers can exhibit bandgap and vibration attenuation properties. However, the bandgap properties of the electromechanical metamaterials are limited by the electromechanical coupling coefficient. In order to effectively overcome this limitation of the locally resonant bandgaps, a locally resonant electromechanical metamaterial beam with piezoelectric actuators and sensors is presented, and the piezoelectric shunting technique and negative proportional feedback control strategy are combined. In this design, both negative capacitance (NC) and inductance (L) are incorporated into the shunt circuits. Then, the classical root locus method is employed to obtain single/multiple bandgaps and particular structural response by arranging the poles and zeros. Finally, the influences of the feedback control gain, the shunt circuit type, and the damping ratio on the bandgap properties and wave propagation behaviors are analyzed. Numerical results demonstrate that the single/multiple bandgaps can be obviously broadened by properly increasing the control gain. Specifically, adding negative capacitance in series to pure inductive circuit can generate wider absolute bandgaps at lower frequencies. The comparison of the frequency response and the bandgap characteristics reveals a very good agreement. Summarily speaking, combining the piezoelectric shunting technique and negative proportional feedback control strategy can effectively tune the vibration and wave propagation behavior.