Figure 3: Numerical studies of acoustic metamaterial waveguide.
(a) FEM simulations of acoustic wave propagation in a 2D discrete metamaterial structure with an array of stainless plates spaced by air gaps. The distance between the air gaps is 1.4 mm and the array periodicity is 3.4 mm. The thickness of plates is 2 mm, and the width of each plate increases from 0.5 to 50 mm with a step of 0.5 mm. The incident acoustic wave is at 7.2 kHz. The pressure field distribution is normalized to the pressure amplitude of the free-space incident plane wave. The colour bar indicates the normalized pressure. (b) The pressure-gain spectra at different positions of the metamaterial for various gap sizes. Other geometric parameters are fixed. The positions (Z1, Z2 and Z3) in the metamaterial structure are chosen to be consistent with those used in Fig. 2. For the discrete metamaterial, the locations Z1, Z2 and Z3 correspond to the centres of gaps 30, 45 and 66 counted from the beginning (z=0) of the tapered metamaterial waveguide, respectively. The pressure-gain spectrum at a specific gap position of the metamaterial is obtained as the pressure field in the gap centre normalized to that of the incident plane wave in the free space. (c) The maximum pressure gain (top) and pressure-gain bandwidth (bottom) with respect to various air gap sizes g obtained at different positions (Z1, Z2 and Z3) of the metamaterials. The maximum pressure gain is obtained as the peak pressure gain in b and the pressure-gain bandwidth is determined by using the full width at half maximum bandwidth of pressure-gain spectrum obtained in b. (d) The directivity patterns of the maximum pressure gain at different working frequencies. The pressure gains are obtained at positions Z1, Z2 and Z3 (that is, gaps 30, 45 and 66), corresponding to the working frequencies at 9.8, 6.8 and 4.5 kHz, respectively. The inset shows the orientation of the metamaterial waveguide with respect to the direction of incident plane waves.
