V. Gupta
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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.
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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.
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.
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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.
Active Piezoelectric Metastructures
Relationship of Bandgap Formation With Unit Cell Number and Modal Behaviour
Elastic piezoelectric metastructures with actively implemented resonators offer an opportunity for novel vibration attenuation solutions, thanks to the possibility of creating bandgaps at low frequencies, their tuneability and compactness. We focus on metastructures with sensors and actuators, where the resonators are implemented using feedback control techniques, an alternative to commonly used shunt circuits. For bandgap creation in finite structures, unit-cell-based dispersion analysis is unsuitable since it lacks information on modal behaviour. As an alternative, a modal analysis approach can be used to calculate the frequency range of a locally resonant bandgap in closed form using the assumption of an infinite number of transducers of infinitesimal length distributed along the structure. The predictions obtained using this approach are accurate if a sufficiently high number of transducers is used, and the number required increases with the increasing target frequency. Despite the recent developments in the field, it remains to be seen what the sufficient number is in a specific situation. In this paper, we show that for low-frequency bandgaps in cantilevers, the minimal number of transducers is equal to the number of the dominant vibration mode at the targeted range of frequencies. Increasing the number of transducers above this value increases the vibration attenuation in the bandgap region but does not result in its widening. The result is demonstrated using numerical analysis.
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Elastic piezoelectric metastructures with actively implemented resonators offer an opportunity for novel vibration attenuation solutions, thanks to the possibility of creating bandgaps at low frequencies, their tuneability and compactness. We focus on metastructures with sensors and actuators, where the resonators are implemented using feedback control techniques, an alternative to commonly used shunt circuits. For bandgap creation in finite structures, unit-cell-based dispersion analysis is unsuitable since it lacks information on modal behaviour. As an alternative, a modal analysis approach can be used to calculate the frequency range of a locally resonant bandgap in closed form using the assumption of an infinite number of transducers of infinitesimal length distributed along the structure. The predictions obtained using this approach are accurate if a sufficiently high number of transducers is used, and the number required increases with the increasing target frequency. Despite the recent developments in the field, it remains to be seen what the sufficient number is in a specific situation. In this paper, we show that for low-frequency bandgaps in cantilevers, the minimal number of transducers is equal to the number of the dominant vibration mode at the targeted range of frequencies. Increasing the number of transducers above this value increases the vibration attenuation in the bandgap region but does not result in its widening. The result is demonstrated using numerical analysis.
Incorporating actively implemented resonators within elastic piezoelectric metastructures presents a unique approach for vibration attenuation, enabling the creation of tuneable low-frequency bandgaps. Through feedback control, we enhance the compactness of these metastructures by integrating resonator dynamics internally. We study the influence of varying the cross-section of the base substrate and the arrangement of transducers on bandgap generation. This influence is captured by the changes in the electromechanical coupling and stiffness of the metastructure, which appear directly in the formulas for bandgap edge frequencies in ideal conditions. This relationship is illustrated with numerical examples for realistic metastructures with a finite number of transducers. Our focus is on metastructures with sensors and actuators, employing feedback control techniques for resonator implementation as an alternative to shunt circuits. When a bandgap is generated in a finite metastructure, its edge frequencies can be calculated in closed form using the assumption of an infinite number of transducers of infinitesimal length distributed along the structure.
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Incorporating actively implemented resonators within elastic piezoelectric metastructures presents a unique approach for vibration attenuation, enabling the creation of tuneable low-frequency bandgaps. Through feedback control, we enhance the compactness of these metastructures by integrating resonator dynamics internally. We study the influence of varying the cross-section of the base substrate and the arrangement of transducers on bandgap generation. This influence is captured by the changes in the electromechanical coupling and stiffness of the metastructure, which appear directly in the formulas for bandgap edge frequencies in ideal conditions. This relationship is illustrated with numerical examples for realistic metastructures with a finite number of transducers. Our focus is on metastructures with sensors and actuators, employing feedback control techniques for resonator implementation as an alternative to shunt circuits. When a bandgap is generated in a finite metastructure, its edge frequencies can be calculated in closed form using the assumption of an infinite number of transducers of infinitesimal length distributed along the structure.