Mechanism of the low-frequency wide-band within a nonlinear acoustic metamaterial

Abstract

In this paper, the formation and broadening mechanism of the low-frequency bandgap are revealed by designing a type of nonlinear acoustic metamaterial (NAM) with gaps. The mechanism of the chaotic evolution through the harmonic coupling for the NAM structure is revealed in detail, which can effectively change spectral characteristics in the bifurcation sequence, and finally, lead to a low frequency and chaos. Then, a low-frequency broadband within the NAM structures with gaps is obtained by the finite element method (FEM) due to the mechanism of chaos. Most importantly, the width of the bandgap can be successfully enlarged by adjusting the small gap, because the energy of the elastic wave can be greatly decreased or redistributed with the system going from periodic motion to doubling bifurcation. This mechanism for achieving a low-frequency bandgap overcomes the shortcomings both in the traditional local resonance with too large additional mass and in the inertial amplification structures with narrow bandgaps. Therefore, this idea of achieving a low-frequency bandgap has great theoretical significance for controlling low-frequency sound waves.