Internally resonant wave energy exchange in weakly nonlinear lattices and metamaterials

Perturbation analysis of nonlinear evanescent waves in a one-dimensional monatomic chain

This paper investigates evanescent waves in one-dimensional nonlinear monatomic chains using a first-order Lindstedt-Poincaré approach. Perturbation approaches applied to traveling waves in similar chains have predicted weakly nonlinear phenomena such as dispersion shifts and amplitude-dependent stability. However, nonlinear evanescent waves have received sparse attention, even though they are expected to serve a critical role in nonlinear interface problems. To aid in their analysis, the nonlinear evanescent waves are categorized herein as either complete or transitional evanescent waves. Complete evanescent waves, including linear evanescent waves, attenuate to zero amplitude in the far field. Transitional evanescent waves, only occurring in softening systems, attenuate to a nontrivial amplitude in the far field, regardless of the initial amplitude, resulting in a saturation effect. For both cases, the presented perturbation approach reveals that the imaginary wave number in the evanescent field is a function of space, rather than a constant value as in its linear counterpart. It also reveals that hardening and softening nonlinearity slow and accelerate the near-field decay, respectively. The predictions obtained from the perturbation approach are verified using numerical simulations with both initial-condition and boundary-continuous excitation, documenting strong agreement.

Experimental proof of emergent subharmonic attenuation zones in a nonlinear locally resonant metamaterial

High-performance locally resonant metamaterials represent the next frontier in materials technology due to their extraordinary properties obtained through materials design, enabling a variety of potential applications. The most exceptional feature of locally resonant metamaterials is the subwavelength size of their unit cells, which allows to overcome the limits in wave focusing, imaging and sound/vibration isolation. To respond to the fast evolution of these artificial materials and the increasing need for advanced and exceptional properties, the emergence of a new mechanism for wave mitigation and control consisting in a nonlinear interaction between propagating and evanescent waves has recently been theoretically demonstrated. Here, we present the experimental proof of this phenomenon: the appearance of a subharmonic transmission attenuation zone due to energy exchange induced by autoparametric resonance. These results pave the path to a new generation of nonlinear locally resonant metamaterials.

Isolated frequencies at which nonlinear materials behave linearly

In this Rapid Communication, we demonstrate that specific frequencies in weakly nonlinear lattices avoid the generation of higher harmonics, and thus the lattices behave linearly. Using a multiple scales analysis, we present plane-wave solutions that persist at only a single frequency and wave number; i.e., whose spatiotemporal production of higher harmonics is remarkably small. We study monatomic and diatomic chains with quadratic and cubic stiffness nonlinearities as example systems. Direct numerical integration of the equations of motion confirms that finite amplitude plane waves assigned to these special frequencies produce negligible higher harmonics when injected into the lattices. Such findings provide new considerations for the operating frequency of nonlinear communications devices, sensors, and transducers for enhanced signal-to-noise ratios.