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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. Physical realization of complex dynamical pattern formation in magnetic active feedback rings

   https://doi.org/10.1088/1367-2630/ac47cb  

   Anderson, Justin Q.; Janantha, P. A. Praveen; Alcala, Diego A.; Wu, Mingzhong; Carr, Lincoln D. (March 2022, New Journal of Physics)

   Abstract We report the clean experimental realization of cubic–quintic complex Ginzburg–Landau (CQCGL) physics in a single driven, damped system. Four numerically predicted categories of complex dynamical behavior and pattern formation are identified for bright and dark solitary waves propagating around an active magnetic thin film-based feedback ring: (1) periodic breathing; (2) complex recurrence; (3) spontaneous spatial shifting; and (4) intermittency. These nontransient, long lifetime behaviors are observed in self-generated spin wave envelopes circulating within a dispersive, nonlinear yttrium iron garnet waveguide. The waveguide is operated in a ring geometry in which the net losses are directly compensated for via linear amplification on each round trip (of the order of 100 ns). These behaviors exhibit periods ranging from tens to thousands of round trip times (of the order ofμs) and are stable for 1000s of periods (of the order of ms). We present ten observations of these dynamical behaviors which span the experimentally accessible ranges of attractive cubic nonlinearity, dispersion, and external field strength that support the self-generation of backward volume spin waves in a four-wave-mixing dominant regime. Three-wave splitting is not explicitly forbidden and is treated as an additional source of nonlinear losses. All observed behaviors are robust over wide parameter regimes, making them promising for technological applications. We present ten experimental observations which span all categories of dynamical behavior previously theoretically predicted to be observable. This represents a complete experimental verification of the CQCGL equation as a model for the study of fundamental, complex nonlinear dynamics for driven, damped waves evolving in nonlinear, dispersive systems. The reported dynamical pattern formation of self-generated dark solitary waves in attractive nonlinearity without external sources or potentials, however, is entirely novel and is presented for both the periodic breather and complex recurrence behaviors. 

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3. Surface Roughness Effects on Self-Interacting and Mutually Interacting Rayleigh Waves

   https://doi.org/10.3390/s21165495  

   Bakre, Chaitanya; Lissenden, Cliff J. (August 2021, Sensors)

   Rayleigh waves are very useful for ultrasonic nondestructive evaluation of structural and mechanical components. Nonlinear Rayleigh waves have unique sensitivity to the early stages of material degradation because material nonlinearity causes distortion of the waveforms. The self-interaction of a sinusoidal waveform causes second harmonic generation, while the mutual interaction of waves creates disturbances at the sum and difference frequencies that can potentially be detected with minimal interaction with the nonlinearities in the sensing system. While the effect of surface roughness on attenuation and dispersion is well documented, its effects on the nonlinear aspects of Rayleigh wave propagation have not been investigated. Therefore, Rayleigh waves are sent along aluminum surfaces having small, but different, surface roughness values. The relative nonlinearity parameter increased significantly with surface roughness (average asperity heights 0.027–3.992 μm and Rayleigh wavelengths 0.29–1.9 mm). The relative nonlinearity parameter should be decreased by the presence of attenuation, but here it actually increased with roughness (which increases the attenuation). Thus, an attenuation-based correction was unsuccessful. Since the distortion from material nonlinearity and surface roughness occur over the same surface, it is necessary to make material nonlinearity measurements over surfaces having the same roughness or in the future develop a quantitative understanding of the roughness effect on wave distortion. 

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4. Nucleation of transition waves via collisions of elastic vector solitons

   https://doi.org/10.1063/5.0156023  

   Yasuda, H; Shu, H; Jiao, W; Tournat, V; Raney, J R (July 2023, Applied Physics Letters)

   In this work, we show that collisions of one type of nonlinear wave can lead to generation of a different kind of nonlinear wave. Specifically, we demonstrate the formation of topological solitons (or transition waves) via collisions of elastic vector solitons, another type of nonlinear wave, in a multistable mechanical system with coupling between translational and rotational degrees of freedom. We experimentally observe the nucleation of a phase transformation arising from colliding waves, and we numerically investigate head-on and overtaking collisions of solitary waves with vectorial properties (i.e., elastic vector solitons). Unlike KdV-type solitons, which maintain their shape despite collisions, our system shows that collisions of two vector solitons can cause nucleation of a new phase via annihilation of the vector solitons, triggering the propagation of transition waves. The propagation of these depends both on the amount of energy carried by the vector solitons and on their respective rotational directions. The observation of the initiation of transition waves with collisions of vector solitons in multistable mechanical systems is an unexplored area of fundamental nonlinear wave interactions and could also prove useful in applications involving reconfigurable structures. 

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5. Broadband Frequency and Spatial On-Demand Tailoring of Topological Wave Propagation Harnessing Piezoelectric Metamaterials

   https://doi.org/10.3389/fmats.2020.602996  

   Dorin, Patrick; Wang, K. W. (January 2021, Frontiers in Materials)

   null (Ed.)

   Many engineering applications leverage metamaterials to achieve elastic wave control. To enhance the performance and expand the functionalities of elastic waveguides, the concepts of electronic transport in topological insulators have been applied to elastic metamaterials. Initial studies showed that topologically protected elastic wave transmission in mechanical metamaterials could be realized that is immune to backscattering and undesired localization in the presence of defects or disorder. Recent studies have developed tunable topological elastic metamaterials to maximize performance in the presence of varying external conditions, adapt to changing operating requirements, and enable new functionalities such as a programmable wave path. However, a challenge remains to achieve a tunable topological metamaterial that is comprehensively adaptable in both the frequency and spatial domains and is effective over a broad frequency bandwidth that includes a subwavelength regime. To advance the state of the art, this research presents a piezoelectric metamaterial with the capability to concurrently tailor the frequency, path, and mode shape of topological waves using resonant circuitry. In the research presented in this manuscript, the plane wave expansion method is used to detect a frequency tunable subwavelength Dirac point in the band structure of the periodic unit cell and discover an operating region over which topological wave propagation can exist. Dispersion analyses for a finite strip illuminate how circuit parameters can be utilized to adjust mode shapes corresponding to topological edge states. A further evaluation provides insight into how increased electromechanical coupling and lattice reconfiguration can be exploited to enhance the frequency range for topological wave propagation, increase achievable mode localization, and attain additional edge states. Topological guided wave propagation that is subwavelength in nature and adaptive in path, localization, and frequency is illustrated in numerical simulations of thin plate structures. Outcomes from the presented work indicate that the easily integrable and comprehensively tunable proposed metamaterial could be employed in applications requiring a multitude of functions over a broad frequency bandwidth. 

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