Extreme Wave Localization in Nonlinear Mechanical Metamaterials

Abstract

Mechanical metamaterials, engineered structures with tailored mechanical properties, have emerged as a powerful platform for manipulating waves, spurring extensive research in both linear and nonlinear wave dynamics. Wave localization—the concentration of energy within specific regions—is central to controlling waves. In the linear regime, topological insulators offer robust wave-guiding through protected boundary states; however, existing designs often exhibit limitations in tunability and energy management.On the other hand, nonlinear wave localization manifests as distinct phenomena such as solitons and rogue waves. Solitons, stable and localized wave packets, hold promise for efficient energy transport and have been extensively studied in optical systems. Conversely, rogue waves, characterized by extreme amplitudes and transient appearances, provide insights into abrupt wave phenomena that typically pose significant challenges for prediction and control in diverse physical systems ranging from oceans to optical fibers. While these nonlinear wave phenomena are well-studied theoretically and numerically, experimental investigations in mechanical metamaterials remain limited, hindering a comprehensive understanding of their behavior and subsequent application in mechanical systems. In this work, we address these limitations by investigating wave localization in mechanical metamaterials across both linear and nonlinear regimes, focusing on manipulating waves and experimentally realizing extreme wave events. For linear waves, we explore topological wave localization using a one-dimensional (1D) dimer lattice with a coupled degree of freedom. Leveraging its inherent axial-rotation coupling, we demonstrate an in situ tunability of the dispersion relationship, enabling a controlled transfer of topologically protected edge states. This coupling-driven energy control is then extended to the nonlinear regime, where we propose a method for manipulating solitary and rogue waves. Experimentally, we first conduct a series of experiments using single-component 1D lattices, quantifying the phase shift from head-on rarefaction soliton collisions to be compared with analytical and numerical estimates. Finally, we experimentally demonstrate rogue wave formation in a mechanical metamaterial using a low-dissipation setup. Gaussian initial profiles are assigned to the lattice to form rogue waves, and the influence of varying initial energy landscapes is examined. We believe that our findings shall provide deeper insight into wave localizations in mechanical metamaterials, paving the way for applications in vibration control, energy harvesting, and extreme event mitigation.