Abstract
The propagation of waves in nonlinear acoustic metamaterial (NAM) is fundamentally different from that in conventional linear ones. In this article we consider two one-dimensional (1D) NAM systems featuring respectively a diatomic and a tetratomic meta unit-cell. We investigate the attenuation of waves, band structures, and bifurcations to demonstrate novel nonlinear effects, which can significantly expand the bandwidth for elastic wave suppression and cause nonlinear wave phenomena. The harmonic averaging approach, continuation algorithm, and Lyapunov exponents (LEs) are combined to study the frequency responses, nonlinear modes, bifurcations of periodic solutions, and chaos. The nonlinear resonances are studied, and the influence of damping on hyperchaotic attractors is evaluated. Moreover, a ‘quantum’ behavior is found between the low-energy and high-energy orbits. This work provides a theoretical base for furthering understandings and applications of NAMs.
Highlights
Like the phononic crystals [1,2], acoustic metamaterials [3,4,5,6] (AMs) are artificial medias that gain their properties from structure rather than composition
A four-cell nonlinear acoustic metamaterials (NAMs) can allow for a homogeneously amplification in a broad passband. Another question we have addressed is: why is the nonlinear locally resonant (LR) bandgap less efficient than other bandgaps to suppress the elastic waves in NAM? To answer this question, we have set the frequencies to Ω=0.35 and Ω=1
We further demonstrate that nonlinear effects can greatly suppress elastic waves in broad frequency ranges
Summary
Like the phononic crystals [1,2], acoustic metamaterials [3,4,5,6] (AMs) are artificial medias that gain their properties from structure rather than composition. Using a perturbation approach and the harmonic balance method, Narisetti et al [40,41] recently studied the amplitude-dependent dispersions, stop band properties, and wave beaming in nonlinear periodic granular media On their side, Manktelow et al.[42] investigated the wave propagation in layered NPS based on a perturbation approach. In the recent works [46][47], the wave propagation in diatomic and tetratomic NAMs are analyzed using the homotopy analysis method, and we found that the chaotic bands resulting from bifurcations can significantly enlarge the width of the forbidden bands This finding demonstrates that chaos is a novel and promising mechanism to achieve simultaneously low-frequency and broad band in both mono-bandgap NAMs and multi-bandgap NAMs and still that a strong nonlinearity is beneficial to expand the bandwidth by several times. In this paper we attempt to answer these questions with the help of the frequency response analysis, the bifurcation theories, the Lyapunov exponents (LEs) and the fractal dimensions
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