A study to realize acoustic cloak using topology optimization based on level-set method.

Abstract

This paper proposed a topology optimization method to realize acoustic cloaking by minimizing scattering waves around a cloaked cylindrical obstacle placed in unbounded air medium. In this study, we develop a two-phase material model mixed with a solid and fluid phases to express an elastic material and an acoustic material in a unified represenation. By applying the model, boundary conditions at boundaries between different two-phase materials are satisfied naturally, and are not needed to be imposed. Then, we formulate an optimization problem to realize acoustic cloak utilizing the two-phase material model and a level set method to express boundaries between different two-phase materials. Topological derivative of an objective functional is considered to be proportional to the derivative of the level set functions with respect to time and the values of the level set functions are updated by solving time evolutionary reaction diffusion equation with a regularization term. An approximate method to obtain topological derivative is also developed by applying the variational analysis and the adjoint variable method. Several numerical demonstrations are presented for directional acoustic cloakings.