Wave propagation in one-dimensional nonlinear acoustic metamaterials

TL;DR

This paper explores wave propagation in one-dimensional nonlinear acoustic metamaterials, revealing novel nonlinear effects, expanded wave suppression bandwidths, and complex bifurcation phenomena through advanced analytical methods.

Contribution

It introduces a comprehensive analysis of nonlinear wave behavior in 1D NAMs with diatomic and tetratomic units, highlighting new nonlinear effects and chaotic dynamics.

Findings

Expanded bandwidth for elastic wave suppression.

Identification of nonlinear resonances and bifurcations.

Discovery of hyper-chaotic attractors and quantum-like behavior.

Abstract

The propagation of waves in the nonlinear acoustic metamaterials (NAMs) is fundamentally different from that in the conventional linear ones. In this article we consider two one-dimensional NAM systems featuring respectively a diatomic and a tetratomic meta unit-cell. We investigate the attenuation of the wave, the band structure and the bifurcations to demonstrate novel nonlinear effects, which can significantly expand the bandwidth for elastic wave suppression and cause nonlinear wave phenomena. Harmonic averaging approach, continuation algorithm, Lyapunov exponents are combined to study the frequency responses, the nonlinear modes, bifurcations of periodic solutions and chaos. The nonlinear resonances are studied and the influence of damping on hyper-chaotic attractors is evaluated. Moreover, a "quantum" behavior is found between the low-energy and high-energy orbits. This work provides an important theoretical base for the further understandings and applications of NAMs.