Figure 2: Sound compression and pressure amplification effects in metamaterial based on analytical model.
(a) Schematic of a tapered metamaterial slab comprised of an array of stainless plates spaced by air gaps with gap distance g=1.4 mm and array periodicity p=3.4 mm. The height and thickness of plates are H=40 mm and t=2 mm, respectively. The width w of each plate increases from 0.5 to 50 mm with a step of 0.5 mm. For simplicity, the metamaterial structure is considered as a 2D system and the propagation of acoustic wave is assumed to be confined in the x–z plane. (b) The wave compression effect in metamaterial. The spatial distribution of neff and the spatial oscillation of normalized pressure field along the wave propagation direction are obtained by using equations (4) and (5) at 7.2 kHz, respectively. The pressure fields inside metamaterial region are normalized by the initial pressure amplitude P(z=0) in equation (5), which is equal to the pressure amplitude of free-space incident wave. (c) Dispersion properties of neff at different locations along the propagation axis (Z1=102 mm, Z2=153 mm and Z3=224 mm). (d) The corresponding pressure-gain spectra at different locations of the metamaterial. The pressure-gain spectrum at specific position z in metamaterial is obtained as P(f,z)/P(f,z=0).
