Broadband and tunable one-dimensional strongly nonlinear acoustic metamaterials: Theoretical study

Abstract

This paper focuses on the dispersion properties and mechanism of the one-dimensional strongly nonlinear acoustic metamaterials (NAMMs) based on the homotopy method. The local bifurcation mechanism, which is different from conventional local resonance, is found. It is demonstrated that the local period-doubling bifurcation of multiple cells will induce chaotic bands in the NAMMs, which can significantly expand the bandwidth for wave suppression. The saddle-node bifurcation leads the system state jumping to the chaotic branch. Furthermore, the amplitude-dependent dispersion properties enable NAMMs to manipulate elastic waves externally. Study of broadband tunable abilities reveals that stronger nonlinearity (larger nonlinear coefficient or higher amplitude) presents a broader nonlinear band gap and larger transmission loss. Moreover, with less attached mass, a low frequency and broadband are achievable simultaneously. This research may provide useful approaches for elastic wave control.

Ultra-low and ultra-broad-band nonlinear acoustic metamaterials

“…The differences between N1 and N2 illustrate that: the periodic Duffing oscillators are responsible for the wave suppression near LR1 but its influence decreases with increasing distance to LR1 (both below and above LR1); and the vibro-impact oscillators are responsible for wave suppression in the two passbands on both sides of LR2 (Supplementary Note 3). As shown by NAM-N2, LR1 becomes a passband and the resonances in the second and the third passbands are substantially reduced because the linear resonances are replaced by the nonlinear resonances with finite amplitude 47 . The experimental results agree well with the theoretical findings here and that from the discrete models 47–49 , supporting the proposed mechanism for nonlinear wave propagation and the band structure of NAMs.…”

“…As shown by NAM-N2, LR1 becomes a passband and the resonances in the second and the third passbands are substantially reduced because the linear resonances are replaced by the nonlinear resonances with finite amplitude 47 . The experimental results agree well with the theoretical findings here and that from the discrete models 47–49 , supporting the proposed mechanism for nonlinear wave propagation and the band structure of NAMs.…”

“…Therefore, the passbands of the strongly nonlinear AMs can significantly attenuate the elastic waves and enables subwavelength properties with a = λ f /9 (see Methods). In the first passband, the influences of the nonlinearity on the three resonances are: significant for 31.56 Hz, moderate for 16 Hz ( H ( ω ) decreases by 8 dB) and weak for 6 Hz ( H ( ω ) unchanged), suggesting that the lower the resonance frequency below LR1, the weaker the effect of the nonlinearity 47, 49 .…”

“…Recently, a mechanism was theoretically predicted in discrete NAMs 47–49 : the chaotic bands. Chaos is an aperiodic long-term behavior in a deterministic/nonlinear system exhibiting a strong dependence on the initial conditions 50 .…”

“…In NAMs 49 , chaotic bands are those passbands in which an incident low-frequency periodic wave becomes a chaotic emerging wave, reducing wave transmission. The chaotic wave features a high-frequency continuous spectrum evidencing the dispersion of energy 47, 49 . These waves have lower amplitudes than the corresponding linear resonances; thus, NAMs can suppress wave propagation in the passbands.…”