Digitally controlled mechatronic metamaterials for actively induced targeted bandgaps

Abstract

Passive elastic metamaterials offer effective vibration attenuation through locally resonant bandgaps, but suffer from fundamental limitations in real-time tunability, narrow operational bandwidth, and non-adaptive behavior. This work presents an experimental framework for inducing and tuning vibration bandgaps in digitally controlled mechatronic metamaterials. A slender-beam structure instrumented with collocated piezoelectric sensor–actuator pairs distributed periodically along the length is used as the host medium, with decentralized second-order low-pass resonant filter with negative position feedback controllers implemented in real time on an FPGA platform. Unlike conventional approaches that assess bandgap formation through tip displacement, this study relies on bending strain minimization of piezoelectric sensors as the principal indicator of control-induced bandgaps. This more accurately reflects the moment-based phase cancellation dynamics underlying resonant actuation. Closed-form analytical expressions for transmissibility in a general $n \times n$ decentralized feedback architecture are derived via block elimination and experimentally validated using the $7\times 7$ unit-cell configuration. The results demonstrate that targeted low-frequency bandgaps in the range of 20–100 Hz can be systematically induced and reshaped through programmable tuning of controller gain and damping ratio, significantly improving vibration attenuation. By shifting the focus to localized dynamics, this work deepens the understanding of how control-induced bandgaps emerge and demonstrates a scalable pathway for designing programmable mechatronic metamaterials based on based on digitally synthesized resonator dynamics.