Digitally Controlled Mechatronic Metamaterials for Actively Induced Targeted Bandgaps

TL;DR

Problem: achieving real-time, programmable vibration bandgaps in elastic metamaterials. Approach: decentralized digital controllers implement second-order low-pass resonant filters with negative position feedback on collocated piezo patches; bending-strain in piezo sensors guides bandgap indication, and an analytical transmissibility expression for an $n \times n$ lattice is derived and validated on a $7 \times 7$ unit-cell beam. Findings: tunable low-frequency bandgaps emerge through localized unit-cell control and inter-cell coupling, with system behavior well predicted by the closed-loop transmissibility framework. Significance: the method enables scalable, reconfigurable metamaterials for active vibration isolation, extending bandgap engineering beyond structural resonances.

Abstract

This paper 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 reflects more accurately the moment-based phase cancellation dynamics similar to resonator behavior. We derive analytical expressions for transmissibility in an n x n decentralized feedback architecture and verify them experimentally using a 7 x 7 unit-cell configuration. The findings show that resonant controllers with negative feedback applied at the unit-cell level can be systematically tuned through controller gain and damping to open targeted low-frequency bandgaps and significantly improve 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 unconventional resonator behavior.

Figures (8)

• Figure 1: (a) Schematic representation of a single unit cell integrated with a collocated actuator–sensor configuration driven through the controller, and (b) representation of a metabeam with the $j^{\text{th}}$ unit cells distributed along its length kaczmarek2024bandgap.
• Figure 2: (a) Fabrication of mechatronic metamaterial beam with piezo actuators and sensors attached back to back surface of the beam, performing soldering, (b) A complete experimental setup for measurement with controllers and testbed, (c) Close-up of beam.
• Figure 3: Closed-loop block diagram of the decentralised control architecture used in active piezoelectric metamaterials.
• Figure 4: Experimental frequency response magnitudes of the considered $7\times 7$ system, open-loop (blue) and simulated closed-loop responses obtained by applying a resonant controller to collocated pairs (red). The collocated responses are diagonally highlighted in yellow.
• Figure 5: Experimental validation of the closed-loop response (blue) compared with the simulated closed-loop response (red).