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1. Introduction of Local Resonators to a Nonlinear Metamaterial With Topological Features

   https://doi.org/10.1115/1.4064726  

   LeGrande, Joshua; Malla, Arun; Bukhari, Mohammad; Barry, Oumar (July 2024, Journal of Computational and Nonlinear Dynamics)

   Abstract Recent work in nonlinear topological metamaterials has revealed many useful properties such as amplitude dependent localized vibration modes and nonreciprocal wave propagation. However, thus far, there have not been any studies to include the use of local resonators in these systems. This work seeks to fill that gap through investigating a nonlinear quasi-periodic metamaterial with periodic local resonator attachments. We model a one-dimensional metamaterial lattice as a spring-mass chain with coupled local resonators. Quasi-periodic modulation in the nonlinear connecting springs is utilized to achieve topological features. For comparison, a similar system without local resonators is also modeled. Both analytical and numerical methods are used to study this system. The dispersion relation of the infinite chain of the proposed system is determined analytically through the perturbation method of multiple scales. This analytical solution is compared to the finite chain response, estimated using the method of harmonic balance and solved numerically. The resulting band structures and mode shapes are used to study the effects of quasi-periodic parameters and excitation amplitude on the system behavior both with and without the presence of local resonators. Specifically, the impact of local resonators on topological features such as edge modes is established, demonstrating the appearance of a trivial bandgap and multiple localized edge states for both main cells and local resonators. These results highlight the interplay between local resonance and nonlinearity in a topological metamaterial demonstrating for the first time the presence of an amplitude invariant bandgap alongside amplitude dependent topological bandgaps. 

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2. Effect of electromechanical coupling on locally resonant quasiperiodic metamaterials

   https://doi.org/10.1063/5.0119914  

   LeGrande, Joshua; Bukhari, Mohammad; Barry, Oumar (January 2023, AIP Advances)

   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. 

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3. On a Nonlinear Locally Resonant Metamaterial With Resistance-Inductance Shunt

   https://doi.org/10.1115/1.4065010  

   Malla, Arun; Bukhari, Mohammad; Barry, Oumar (May 2024, Journal of Computational and Nonlinear Dynamics)

   Abstract Numerous recent works have established the potential of various types of metamaterials for simultaneous vibration control and energy harvesting. In this paper, we investigate a weakly nonlinear metamaterial with electromechanical (EM) local resonators coupled to a resistance-inductance shunt circuit, a system with no previous examination in the literature. An analytical solution is developed for the system, using the perturbation method of multiple scales, and validated through direct numerical integration. The resulting linear and nonlinear band structures are used for parametric analysis of the system, focusing on the effect of resonator and shunt circuit parameters on band gap formation and vibration attenuation. This band structure analysis informs further study of the system through wavepacket excitation as well as spectro-spatial analysis. The voltage response of the system is studied through spatial profiles and spectrograms to observe the effects of shunt inductance, nonlinearity, and their interactions. Results describe the impact of adding a shunted inductor, including significant changes to the band structure; multiple methods of tuning band gaps and pass bands of the system; and changes to wave propagation and voltage response. The results demonstrate the flexibility of the proposed metamaterial and its potential for both vibration control and energy harvesting, specifically compared to a previously studied system with resistance-only shunt. 

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4. Mass conserved metastructure for vibration suppression via bandgap tuning

   Colford, Greta P; Wang, Kon_Well; Inman, Daniel J (May 2025, Mechanical systems and signal processing)

   Architected materials can be synthesized to effectively control elastic wave propagation via bandgap engineering, which is essential for vibration mitigation and sound attenuation applications. Mechanisms for controlling elastic waves include Bragg scattering resulting from structural periodicity and local resonance effects, both of which were employed to create bandgaps. It is also shown that with careful design, the Bragg- and resonance-type bandgaps can be combined to achieve broader stopbands. Structures that use these bandgap mechanisms, especially those utilizing local resonators, add mass to the system, which could be highly undesirable for many engineering applications where mass considerations directly impact the system efficiency. To address this shortfall and advance the state of the art, this research proposes a mass-conserved design concept for metastructures that utilize both Bragg-type and local resonance bandgap mechanisms to create enhanced bandgap characteristics within the structure. The mass-conserved design is achieved by employing the existing system mass to create geometries that allow for bandgap generation, rather than adding mass to the structure as seen in traditional metastructure systems. The developed methodology shows that broader stopbands can be created without adding mass to the overall system, and this research identifies critical design parameters in order to achieve effective mass-conserved bandgap engineering compared to traditional metastructures designs. This method of mass-conserved metastructure design is shown to be effective when applied to various means of tuning that further enhance the bandgap regions, including the use of multiple-degree-of-freedom resonators and hybrid unit cells. These advancements provide a mass-constrained approach to bandgap engineering methods, expanding our ability to create lighter and more efficient structures with effective vibration control. 

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5. Sharkskin-Inspired Magnetoactive Reconfigurable Acoustic Metamaterials

   https://doi.org/10.34133/2020/4825185  

   Lee, Kyung Hoon; Yu, Kunhao; Al Ba’ba’a, Hasan; Xin, An; Feng, Zhangzhengrong; Wang, Qiming (February 2020, Research)

   Most of the existing acoustic metamaterials rely on architected structures with fixed configurations, and thus, their properties cannot be modulated once the structures are fabricated. Emerging active acoustic metamaterials highlight a promising opportunity to on-demand switch property states; however, they typically require tethered loads, such as mechanical compression or pneumatic actuation. Using untethered physical stimuli to actively switch property states of acoustic metamaterials remains largely unexplored. Here, inspired by the sharkskin denticles, we present a class of active acoustic metamaterials whose configurations can be on-demand switched via untethered magnetic fields, thus enabling active switching of acoustic transmission, wave guiding, logic operation, and reciprocity. The key mechanism relies on magnetically deformable Mie resonator pillar (MRP) arrays that can be tuned between vertical and bent states corresponding to the acoustic forbidding and conducting, respectively. The MRPs are made of a magnetoactive elastomer and feature wavy air channels to enable an artificial Mie resonance within a designed frequency regime. The Mie resonance induces an acoustic bandgap, which is closed when pillars are selectively bent by a sufficiently large magnetic field. These magnetoactive MRPs are further harnessed to design stimuli-controlled reconfigurable acoustic switches, logic gates, and diodes. Capable of creating the first generation of untethered-stimuli-induced active acoustic metadevices, the present paradigm may find broad engineering applications, ranging from noise control and audio modulation to sonic camouflage. 

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