Broadband solid cloak for underwater acoustics

Shielding an object to be undetectable is an important issue for engineering applications. Cloaking is the ultimate shielding example, routing waves around an object without mutual interaction, demonstrated as possible in principle by transformation and metamaterial techniques. Example applications have been successfully designed and validated for electromagnetic wave, thin plate flexural wave, thermal flux, and airborne sound. However, for underwater acoustics, the commonly used scheme based on meta-fluids with anisotropic density for airborne sound is unworkable since an acoustic rigid material is required with mass density three orders of magnitude higher than water. Material with such high density is impossible using even the heaviest metal, and may suffer from a narrow working frequency band even if realized with locally resonant techniques. In any case, such cloak would be inherently fluid with only limited practical interest. An alternative solution was recently suggested based on solid pentamode material, which can be impedance matched with water and has anisotropic modulus. A cloak constructed from this material was theoretically shown to have broadband frequency range effect, and sufficient solidity to be potentially suitable for underwater applications. Here, we report an underwater solid cloak with broadband efficiency utilizing pentamode material machined from aluminum. The cloak was composed with a graded subwavelength scale microstructure to meet the required effective property designed by transformation method. Transient wave experiments conducted in a waveguide validate cloaking effectiveness: the underwater acoustic wave is guided around the cloaked object with substantial reduction of both scattering and shadow over a broad frequency range. This finding paves the way for controlling underwater acoustics using achievable and available metamaterials with broadband efficiency, and may stimulate development of new technologies, such as directed communications, advanced detection systems, or cloaking devices against underwater acoustics. Cloaking as an ultimate shielding example, demonstrated as possible in principle by transformation and metamaterial technique, has been successfully designed for different physical fields. As for air-borne sound, acoustic ground cloaks have been experimentally demonstrated using perforated plates in air, which serves as the meta-fluid with anisotropic density. However, this material design scheme is unsuitable for dense fluids such as water due to the enormous material density required, preventing underwater acoustic cloaking from being realized. Solid material cloaking is highly desired, but the difficulty lies in different propagating velocities for longitudinal and shear waves coexistent in a solid, which are hard to control simultaneously. Tailoring the material deformation modes through microstructure design allows five easy deformation modes, enabling a single pseudo pressure wave. This pentamode (PM) material acts as a meta-fluid with anisotropic modulus realized by the micro structured solid. PM material can be impedance matched with water and provide much larger achievable modulus anisotropy than available through just density variations, offering unprecedented flexibility for underwater acoustic control. Underwater cloaks have been designed based on PM material using transformation approach, and shown to have broadband effects from a solid shield which is particularly suitable for underwater applications. However, experiment demonstration has not been reported due to lack of microstructure design and measurement systems for 2D underwater waveguide. This study reports an underwater solid cloak composed of five graded PM material layers. Transient wave experiments conducted in a specially designed 2D underwater waveguide validated superior wave shielding performance of the designed cloak, with 6.3 dB average reduction of target strength achieved across a broad frequency band 9–15 kHz. Figure 1a shows the fabricated cylindrical cloak, machined from aluminum block using advanced electrical discharge machining (EDM) technique with high accuracy. The fabricated cloak had inner diameter 200mm; outer diameter 334 mm; height 50 mm; and mass 4.87 kg, which is quite close to the mass of an ideal cloak (4.42 kg). The cloak consisted of 50 sectors of cells around the θ-direction, and a zoomed sector in Fig. 1b (bounded by red lines) shows five graded unit cells along the r direction. Calibrating six geometric parameters of the proposed unit cell (Fig. 1c), effective moduli, Kθ and Kr, and density, ρ, of each layer were tuned to provide the derived optimized material anisotropy and property gradient (Fig. 1d, 1e). Modulus anisotropy, Kθ/Kr, increases from outer to inner sides, reaching 40 for the first two layers, while the outermost layer is nearly impedance matched with water (Zcloak/Zwater=0.94, Z represents impedance). A relatively thin cloaking shell and coarse layer optimized discretization is chosen to facilitate fabrication while still achieving broadband shielding performance due to the strong anisotropy of the proposed unit cell. (See Methods, Table S1,