Topological design of lattice materials with application to underwater sound insulation

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Lattice materials with low acoustic impedance can be treated as acoustic soft boundaries compared to water and have potential application to underwater sound insulation. However, limited by the intuitive design method, only a few simple topologies have been reported, leaving a huge design space and potential performance of lattice materials untapped. This paper shows that lattice materials with low acoustic impedance can be systematically designed using topology optimization combined with the homogenization method. Aside from the material occupation, the azimuth of lattice material as an additional design variable is added to the optimization formulation. By imposing different effective modulus constraints, the results show that two types of bi-mode lattice materials can achieve extremely low acoustic impedance alongside an optimal azimuth. The first type of bi-mode lattice material possesses strong anisotropy and a positive Poisson’s ratio, whereas the second has weak anisotropy and a negative Poisson’s ratio. The optimal azimuth for minimum acoustic impedance is dependent on the degree of anisotropy of bi-mode materials. The minimum value of acoustic impedance is associated not only with the degree of anisotropy but also with feature parameters related to easy-deformation mode. Based on the topology optimized lattice materials, various acoustic metascreens with deep sub-wavelength thickness are proposed to shield underwater sound in a low and broad frequency range. Finally, two samples among the designed acoustic metascreens are fabricated and tested in a water-filled tube. Despite that the thickness of both metascreens is only 17 mm, the experimental results show that the sound transmission is reduced averagely by over 17 dB from 500 Hz to 2000 Hz.