Optimum design of an acoustic metamaterial with negative bulk modulus in an acoustic‐elastic coupled system using a level set–based topology optimization method

Abstract

This paper presents a level set-based topology optimization method for the design of an acoustic metamaterial with negative bulk modulus in an acoustic-elastic coupled system. To represent the coupled system, we propose a two-phase material model in which the solid and acoustic phases are mixed. This model allows the coupled system to be represented uniformly and avoids the need to impose the coupling conditions typically required in analyses of acoustic-elastic coupled systems. The effective bulk modulus of the acoustic metamaterial is represented using an S-parameter-based method and the optimization problem is formulated as a level set-based topology optimization. The topological derivatives for the two-phase material model are obtained using the relationship between the topological and shape derivatives. Numerical examples demonstrate the validity of the proposed two-phase material model and topological derivatives, and an optimal unit cell design for an acoustic metamaterial with negative bulk modulus is obtained at a targeted frequency. KEYWORDSacoustic metamaterial, level set-based topology optimization method, negative bulk modulus, topological derivative, two-phase material model Recently, acoustic metamaterials have been investigated on the basis of certain analogous properties of acoustic and electromagnetic waves. After Liu et al 6 first described a sonic crystal composed of lead, silicone rubber, and epoxy that exhibits acoustic bandgaps, a variety of acoustic metamaterials were proposed, such as those with a negative bulk modulus 7 or a negative refractive index, 8,9 and it is expected that acoustic metamaterials can be used to make functional acoustic devices such as acoustic cloaks 10 and acoustic superlenses. 11

Material parameter optimization for interior and exterior fluid‐structure acoustic problems

“…In most of these problems, the fluid was also treated as a “solid” with negligible shear modulus. In addition, the interface was defined implicitly using a level‐set function 14‐16 or a binary density function in the case of the solid isotropic material penalization (SIMP) approach 17,18 …”

Isogeometric topology optimization of anisotropic metamaterials for controlling high‐frequency electromagnetic wave

“…Thus, several researches have employed the S‐parameter retrieval for obtaining the optimal topologies of metamaterials with a high dispersion property that leads to negative components of the material tensor (see, eg, References for the combination with the LTO using metallic and dielectric materials, respectively). Also, Noguchi et al adopted the S‐parameter retrieval for obtaining acoustic metamaterials possessing a negative bulk modulus. However, the S‐parameter retrieval is not always suitable for evaluating the anisotropic propagation characteristics, as its applicability is limited to the condition that the incident wave is assumed to be perpendicular to the metamaterial's surface.…”

Topology optimization of periodic lattice structures taking into account strain gradient

“…in periodic microstructures, to design high performance materials [12][13][14][15][16][17][18][19][20] or materials with properties not found in nature (negative Poisson's ratio, zero compressibility, negative bulk modulus, etc. (see [21][22][23][24][25]) or complex multiphysics problems [26,27]. These techniques are based on optimizing the homogenized properties of the representative volume element, and using numerical solving methods like finite element to compute the homogenized properties [28], given one geometry of the phases and their microscopic properties.…”