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The study of nonreciprocal wave propagation is of great interests for both fundamental research and engineering applications. Here we demonstrate theoretically and experimentally a bidirectional, nonreciprocal, and high-quality diode that can rectify elastic waves in both forward and backward directions in an elastic metamaterial designed to exhibit enhanced nonlinearity of resonances. This diode can preserve or vary frequency, rectify low-frequency long wave with small system size, offer high-quality insulation, can be modulated by amplitude, and break reciprocity of both the total energy and fundamental wave. We report three mechanisms to break reciprocity: the amplitude-dependent bandgap combining interface reflection, chaotic response combining linear bandgap, amplitude-dependent attenuation rate in damping diode. The bidirectional diode paves ways for mutually controlling information/energy transport between two sources, which can be used as new wave insulators., Comment: 11 pages, 13 figures

Material band structure is key foundation for various modern technologies, but it was regarded as a space-time invariant feature. Acoustic metamaterials show extraordinary properties for processing elastic waves, but conventional realizations suffer from narrow bandgaps. Here we first report a nonlinear acoustic metamaterial whose band structure self-adapts to the propagation distance/time and the bandgap exhibits a self-growing behaviour stemming from giant nonlinear interaction. This space-time self-modulating characteristic highlights an unconventional understanding of the band structure, and the self-growth generates an ultralow and ultrabroad bandgap that breaks through the limitation of the mass law for linear locally resonant bandgaps. We also elucidate the self-adaptive mechanisms. This first demonstration sheds light on conceiving advanced devices and metamaterials with broadband, space-time variant bandgaps for wave self-manipulation.

Nonlinear acoustic metamaterial (NAM) initiates new fields for controlling elastic waves. In this work, the flexural wave propagation in the half-infinite NAM beam consisting of periodic Duffing resonators is reported by considering the third harmonic generation (THG). Different analytical methods are proposed to describe the wave propagation in the equivalent homogenous medium. Then their effectiveness and accuracy are demonstrated in comparison with the finite element methods. We unveil analytically and numerically extensive physical properties of the strongly nonlinear AM, including the nonlinear resonance in a cell, the effective density, nonlinear locally resonant (NLR) bandgap, propagations and couplings of the fundamental and the third harmonics. These characteristics are highly interrelated, which facilitates the prediction of functionalities. In the near field, the identical bifurcation frequency of these features acts as the start frequency of the NLR bandgap for fundamental waves, whose width is narrower for a stronger nonlinearity. While in the far field, the NLR bandgap characterizes a distance-amplitude-dependent behavior leading to a self-adaptive bandwidth. Moreover, the transmission in the passband of the infinite NAM is different from the chaotic band effect of finite NAMs, and it is influenced by the shifted NLR gap. Our work will promote future studies and constructions of NAMs with novel properties.

Nonlinear acoustic metamaterials (NAMs) open new freedoms in exploiting novel technologies for wave manipulations. Recently, the desired ultra-low and ultra-broad-band wave suppressions were achieved by the chaotic bands in NAMs [Nature Commun. 8, 1288 (2017)]. This work describes a remote interaction mechanism in NAMs-bridging coupling of nonlinear locally resonant bandgaps. Bridging bandgaps generate chaotic bands and share the negative mass between nonlinear resonators. The bandwidth and the efficiency for the wave reduction in chaotic bands can be manipulated effectively by modulating the frequency distance between the bridging pair. Theoretical analyses on the triatomic model containing two nonlinearly coupled resonances clarify the principle of bridging bandgaps. NAM beams are created to demonstrate this mechanism experimentally by including the bifurcations of periodic solutions. Our study extends the content of NAMs and more nonlinear effects are anticipated based on this mechanism.

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.