Porous-Solid Metaconverters for Broadband Underwater Sound Absorption and Insulation

Existing solid composite structures composed of several viscoelastic materials and metals mainly exploit diverse resonances, damping, and scattering to realize underwater acoustic wave functionalities. However, low-frequency broadband underwater sound absorption and insulation are still hard to capture with an acoustic coating possessing subwavelength thickness and lightweight nature simultaneously. This paper reports the systematic simulated and experimental validations of a porous-solid underwater metaconverter, consisting of a rubber layer and a topology-optimized elastic metasurface to exhibit broadband functionalities of sound absorption and insulation caused by the strong reflective and transmitted longitudinal-to-transverse wave conversion, while sustaining broadband impedance matching. Various results confirm the predicted capabilities of underwater broadband high-efficiency sound absorption (>80%) or insulation (20 dB) within the range of 2–10 kHz for a large- and limited-size sample, providing an estimate of the energy-converting effect and phenomenon. The present study provides possibilities for elastic wave energy dissipation, harvesting, and underwater acoustic stealth via metasurfaces.

Figure 1

Schematic of a double-layer underwater metaconverter. (a) Illustration of the metaconverter, consisting of a rubber layer (2 cm) and elastic metasurface made of aluminum (2 cm). Metaconverter fixed on steel backing (3 cm) can absorb most of the energy of the incident forward waves or isolate the energy of incident backward waves below the steel backing. (b) Sketch of the vibration modes of the rubber layer to enable sound absorption (upper) or sound insulation (lower). (c) Transmission spectra of L and T waves through the rubber layer with density = 950 kg/m³, Poisson ratio = 0.49, Young’s modulus = 1.4 × 10⁸ Pa, and structural loss factor = 0.2. Background solids without damping have the same material (density, Poisson ratio, and Young’s modulus) parameters as rubber. Dimensions of the metasurface microstructure along the x, y, and z directions are 1, 1, and 50 cm, respectively.

Figure 2

Elastic scattering features and transverse-wave motion induced by mode conversion, considering the periodic boundary condition. Model (a) and scattering parameters S_LL and S_LT (b) for wave reflection. Model (c) and scattering parameters $S_{LL}^{\ast }$ and $S_{LT}^{\ast }$ (d) for wave transmission. (e) Vibration mode at 2900 Hz for wave reflection with maximal conversion. Nonreflecting and fixed boundary conditions are applied on the left and right edges of the model in (a). Nonreflecting boundary conditions are applied on the left and right edges of the model in (c). Color represents the displacement amplitude.

Figure 3

Dynamic properties and wave responses of the metaconverter. (a) Measured frequency-dependent storage modulus and loss factor of the rubber by dynamic mechanical analysis testing. (b) Simulation model for characterizing sound absorption (left) and insulation (right) of the double-layer metaconverter. All thicknesses of the rubber, metasurface, and steel layers are 2 cm. Left and right models represent forward (+) and backward (−) incidences, respectively. (c),(d) Sound absorption and insulation curves with different material parameters and incident waves. Both the constant (Ru_C) and measured frequency-dependent (Ru_E) moduli are adopted to characterize the property of the rubber layer. Simulation based on steel backing (S) is also presented for comparison. Simulated acoustic pressure and total displacements fields at representative frequencies within 2000–10 000 Hz for sound absorption (e) and insulation (f). Fields are extracted from the results using 2-cm-thick rubber with measured parameters in (a).

Figure 4

Sound absorption and insulation of the model without a rubber layer. (a),(b) Absorption curve (+Meta-steel) and acoustic field of the model containing only rubber and steel backing. (c),(d) Insulation curve (−Meta-steel) and acoustic field of the model containing only the metasurface and steel backing. For comparison, the results of the metaconverter (+Ru_E-2 cm, −Ru_E-2 cm) are presented as well.

Figure 5

Sound absorption and insulation of the model without a metasurface layer. (a),(b) Absorption curve (+Ru-steel) and acoustic field of the model containing only rubber and steel backing. (c),(d) Insulation curve (−Ru-steel) and acoustic field of the model containing only rubber and steel backing. For comparison, the results of the metaconverter (+Ru_E-2 cm, −Ru_E-2 cm) are presented as well.

Figure 6

Scattering property of acoustic wave fields. (a) Schematic of the model for scattering characterization. Response is extracted from the semicircle 1 m from the metaconverter. (b) Acoustic pressure distribution in polar coordinates. (c) Acoustic scattering maps at representative frequencies.

Figure 7

Characterization of wave energy inside the metaconverter for sound absorption. Strain energies of L- $({\tilde{e}}_L)$ and T-wave $({\tilde{e}}_T)$ modes inside the rubber layer (a) and elastic metasurface (b). Energy fields of the rubber layer (c) and elastic metasurface (d) at several representative frequencies. Four inserted pictures show the enlarged local fields of the metasurface. Most of T- and L-wave energies are mainly located in the small solid blocks and thin connections, respectively.

Figure 8

Characterization of wave energy inside the metaconverter for sound insulation. Strain energies of two wave modes inside the rubber layer (a) and elastic metasurface (b). Energy fields of the rubber layer (c) and elastic metasurface (d) at several representative frequencies. Four inserted pictures show enlarged local fields of the metasurface. Like the distributions in Fig. 7, most of the T- and L-wave energies are mainly located in the small solid blocks and thin connections, respectively.

Figure 9

Sound absorption and insulation of the metaconverter without loss. (a) Absorption curve (No loss) of the model in which rubber has no loss factor. (b) Insulation curve (No loss) of the model in which rubber has no loss factor. For comparison, the results of the metaconverter (+Ru_E-2 cm, −Ru_E-2 cm) are presented as well.

Figure 10

Measured underwater acoustic functionalities of the metaconverter. (a) Sample with a rubber layer (40 × 50 × 2 cm³) and an aluminium plate (40 × 50 × 2 cm³), which is attached to the steel backing (40 × 50 × 3 cm³). Two side views of the sample and local enlarged picture are displayed. (b) Underwater experimental sets. Two hydrophones are marked by H1 and H2, respectively. Signal is generated by the underwater transducer in front of H1 and received by H1 and H2. Measured (expt.) and simulated (sim.) sound-absorption coefficients (c) and sound-transmission-loss coefficients (d). Acoustic waves incident from the left side of the rubber layer for cases of both sound absorption and insulation. (e) Measured time-domain results at four representative incident pulse signals with center frequencies of 3 kHz, 6, 8, and 10 kHz.

Figure 11

Schematic of propagation of wave signals. (a) Dimensions of the pressure cylinder. (b),(c) Ways wave signals reflect. Primary values are d₁= 1.15 m, d₂= 0.99 m, and d₃= 2.72 m.