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

Summary 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.