SUBJECT: Ph.D. Proposal Presentation
BY: Christopher Sugino
TIME: Thursday, May 10, 2018, 9:00 a.m.
PLACE: Love Building, 109
TITLE: Dynamics of Mechanical and Electromechanical Locally Resonant Metastructures
COMMITTEE: Dr. Alper Erturk, Chair (ME)
Dr. Massimo Ruzzene (ME/AE)
Dr. Levent Degertekin (ME/ECE)
Dr. Aldo Ferri (ME)
Dr. Laurence Jacobs (ME/CE)
Dr. Yang Wang (CE)


Locally resonant (LR) elastic/acoustic metamaterials enable bandgap formation at wavelengths much longer than the lattice parameter for low frequency vibration/sound attenuation. Mechanical LR metamaterials are based on unit cells hosting mass-spring elements as resonating components, whereas their electromechanical counterparts, in the context of this work, leverage piezoelectric unit cells shunted to inductive circuits. Existing modeling and analysis approaches for LR metamaterials have been mostly focused on band structure analysis for waves propagating in an infinite metamaterial that comprises a perfectly periodic lattice arrangement by neglecting the effects of boundary conditions. However, for real-world implementation of LR metamaterial concepts at low frequencies, the formation of LR bandgaps in infinite metamaterials must be reconciled with the interactions between the local resonators and the vibrational modes of finite structures. To this end, the proposed work aims to establish a general framework for analyzing both mechanical and electromechanical LR metastructures, and explicitly obtains the LR bandgap in closed form under the assumption of an infinite number of resonators. Because the analysis is based on a finite structure, it leads to new insights regarding the required number of resonators, resonator placement, and mode shapes of the metastructure, while still yielding the intended metamaterial-type performance for a sufficient number of resonators. Using a modal analysis approach, theoretical and experimental developments are presented for (1) general mechanical metastructures; (2) electromechanical metastructures; and (3) hybrid mechanical-electromechanical metastructures that leverage LR dynamics. It is observed that the bandgap size in the mechanical LR metastructures depends on the added mass due to the resonators, while the bandgap in the electromechanical counterpart is mainly controlled by the system-level electromechanical coupling. Electromechanical metastructures employing piezoelectric unit cells that are shunted to general synthetic impedance shunts offer a new avenue to enable various phenomena, such as enabling bandgaps wider than LR ones as well as multiple bandgap formation. Digital shunt circuit concepts are explored to enable fully programmable metastructures that can leverage both tunable performance and reconfigurable bandgaps. Ongoing efforts include the experimental realization of such piezoelectric metastructures.