Optimal Design of Reactive Acoustic Devices Using Topology Optimization and Binary Variables

Topology optimization of reactive acoustic devices using continuous relaxation methods, such as SIMP, frequently yields intermediate (gray) material densities. These intermediate states do not represent the physical interaction between air and a rigid solid, hindering the interpretation and the manufacturing of the optimized designs. This work presents a purely binary topology optimization framework for the design of reactive acoustic devices, in which a multi-frequency sound pressure level minimization problem, subject to volume and perimeter bounds and to local topological constraints, is solved by a Sequence of Integer Linear Programs. Robustness is obtained by an adaptive trust-region strategy fully decoupled from the volume constraint and by relaxing the local topological constraints with continuous slack variables and exact penalty. Exact gradients are provided by a complex-variable adjoint sensitivity analysis of the damped harmonic wave equation. Numerical examples in 2D and 3D produce strictly black-and-white designs with significant broadband attenuation and reveal that the volume bound acts as a budget for wall thickness and reactive inclusion sizing, remaining naturally inactive at the optimum.