Fig. 1.
Schematic and conceptual diagram. a Diatomic NAM model composed of periodic linear base m b coupled with Duffing oscillators m r through the nonlinear spring k 1 x + k 2 x 3, where k 1 and k 2 are the linear and nonlinear stiffness coefficients, respectively. b Its band structure. Here, the passbands become chaotic bands, where a periodic input wave u in generates chaotic output wave (u out red) with an amplitude is much lower than that of the corresponding linear resonance (u out dashed black). c Two nonlinear sources in our NAM cell: Duffing oscillator and coupled vibro-impact system (m c couples to J r through a linear spring k 3 and with a clearance δ). d Conceptual diagram of the double-ultra mechanism using chaotic bands. LR1 (LR2) represents the first (second) LR bandgap induced by the linearized Duffing and vibro-impact systems, respectively. The black (dashed black) arrow represents the input wave u in (its transmission) in linear resonant passbands and the red arrows represent the frequency components in the chaotic wave u out. In b, d, the light blue (white) areas represent the band structure of the NAM (the corresponding LAM), where the blue lines are the upper limits of the chaotic bands