Research / 2021 / Article / Fig 3

Research Article

Tunable Fluid-Type Metasurface for Wide-Angle and Multifrequency Water-Air Acoustic Transmission

Figure 3

The parallel and series mass-spring model for predicting the . (a) Schematic illustration of the FAM with different bubble sizes. Every bubble in the cells is numbered. The th bubble has the side lengths of and , and the wall thickness is , thus, the parameters for th bubble can be marked as (, , ). (b) The structure in a can be treated as the parallel mass-spring system. The and are the effective mass and effective spring constant, respectively. (c) Schematic illustration of the multilayer structure of (a). The structure has layer FAMs, and each water layer is numbered. (d) The structure in can be treated as the series mass-spring system. (e) The energy transmission coefficient vs. frequency by the FEM and analytical solution in Note S3 for . The mass-spring models indicate the different modes of vibration at the corresponding resonant frequency. (f) The energy transmission coefficient vs. frequency for obtained by the FEM calculations and the analytical solution from equations (4) and (5). The analytical solution predicts the frequencies of very well.