Electromechanical metamaterials have been the focus of many recent studies for use in simultaneous energy harvesting and vibration control. Metamaterials with quasiperiodic patterns possess many useful topological properties that make them a good candidate for study. However, it is currently unknown what effect electromechanical coupling may have on the topological bandgaps and localized edge modes of a quasiperiodic metamaterial. In this paper, we study a quasiperiodic metamaterial with electromechanical resonators to investigate the effect on its bandgaps and localized vibration modes. We derive here the analytical dispersion surfaces of the proposed metamaterial. A semi-infinite system is also simulated numerically to validate the analytical results and show the band structure for different quasiperiodic patterns, load resistors, and electromechanical coupling coefficients. The topological nature of the bandgaps is detailed through an estimation of the integrated density of states. Furthermore, the presence of topological edge modes is determined through numerical simulation of the energy harvested from the system. The results indicate that quasiperiodic metamaterials with electromechanical resonators can be used for effective energy harvesting without changes in the bandgap topology for weak electromechanical coupling.
We consider a discrete non-linear Schrödinger equation on Z and show that, after adding a small potential localized in the time-frequency space, one can construct a three-parametric family of non-decaying spacetime quasiperiodic solutions to this equation. The proof is based on the Craig–Wayne–Bourgain method combined with recent techniques of dealing with Anderson localization for two-dimensional quasiperiodic operators with degenerate frequencies.
more » « less- PAR ID:
- 10498019
- Publisher / Repository:
- AIP
- Date Published:
- Journal Name:
- Journal of Mathematical Physics
- Volume:
- 65
- Issue:
- 1
- ISSN:
- 0022-2488
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0166183
