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Abstract We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our experiments, we arrange a lattice in a hexagonal configuration with a light-mass defect, and we harmonically drive the center of the chain with a tunable excitation frequency, amplitude, and angle. We use a damped, driven variant of a vector Fermi–Pasta–Ulam–Tsingou lattice to model our experimental setup. Despite the idealized nature of this model, we obtain good qualitative agreement between theory and experiments for a variety of dynamical behaviors. We find that the spatial decay is direction-dependent and that drive amplitudes along fundamental displacement axes lead to nonlinear resonant peaks in frequency continuations that are similar to those that occur in one-dimensional damped, driven lattices. However, we observe numerically that driving along other directions results in asymmetric NLMs that bifurcate from the main solution branch, which consists of symmetric NLMs. We also demonstrate both experimentally and numerically that solutions that appear to be time-quasiperiodic bifurcate from the branch of symmetric time-periodic NLMs. 

Abstract Acoustic non-reciprocity, referring to the phenomenon of path-dependent propagation, has diverse applications in mechanical devices. This paper presents a numerical study on a periodic triangle-shape structure that breaks reciprocity in a passive manner over a broad range of frequency and energy. The proposed structure contains strong nonlinearity and geometric asymmetry, which contributes to a direction-dependent dispersion relationship. When the signal frequency falls in the band pass in one direction, and band gap in the other, a unidirectional wave propagation results. The system achieves giant non-reciprocity with minimal distortion in the frequency content of the signal. 

We investigate wave propagation in in-plane rotator lattices and demonstrate dispersion morphing and extreme acoustoelastic effects using analytical and numerical means. By changing the angle of the rotator arms attaching the elastic linkage between adjacent rotators, we show that the band structure may morph from a positive/negative-group-velocity passband into a flat band across the whole wavenumber space, and then into a negative/positive-group-velocity passband. A similar process can also occur at certain fixed arm angles when the lattice constant changes, which one may interpret as stretching or compressing the structure along the lattice directions, effectively mimicking the acoustoelastic effect. We analytically investigate both processes and provide closed-form expressions for the occurrence of flat bands, which indicates the transition of the passband property. Further, we explore a chiral rotator lattice design where the oscillation equilibrium position for each rotator may shift upon the change of the lattice constant. This design has a unique advantage that the morphed passband maintains approximately the same frequency range such that a signal may stay propagating during the process of dispersion morphing. In the end, we present numerical simulations for three potential applications utilizing the aforementioned findings. In these applications, both static and dynamic lattice stretching are considered, resulting in on-demand bi-directional wave-guiding, refraction bending, and time-modulated amplifying. Numerical simulations document a high-quality agreement with theory and yield promising results that may inspire next-generation reconfigurable metamaterials. 

Nonlinear lattices and the nonlinear acoustics they support have a broad impact on shock and vibration mitigation, sound isolation, and acoustic logic devices. In this work, we experimentally study wave redirection, localization, and non-reciprocity in an asymmetric network of two nonlinear lattices with weak linear inter-lattice coupling. We report on the design, fabrication, and system identification of coupled lattices with essentially nonlinear next-neighbor intra-lattice coupling and on their unusual nonlinear acoustics. By weakly coupling the lattices and introducing structural disorder in one of them, we experimentally prove the realization of irreversible breather redirection between lattices governed by a macroscopic analog of the quantum Landau–Zener tunneling effect. In the experiments performed, the input energy is applied by impulse (broadband) excitation, and the resulting acoustical mechanism for wave redirection is in the form of propagating breathers, that is, localized oscillating wave packets formed by the synergy of nonlinearity and dispersion. Moreover, we study the non-reciprocal acoustics of the experimental lattice system by applying separate impulses at each of its four terminals and investigate the tunability with the energy of the resulting acoustic non-reciprocity by systematically varying the impulse intensity. The reported experimental results show that the weakly coupled, disordered, and nonlinear lattice system has wave tailoring properties that are tunable with energy. Altogether, the experimental results agree well with theoretical predictions reported in a companion work based on reduced-order numerical models and prove the efficacy of the system for applications, providing a path for applying these advanced concepts in future structures and devices.