Acoustic topology optimization using a mixed formulation and a three-material scheme

Topology optimization (TO) has demonstrated significant efficacy in generating innovative designs to minimize acoustic or elastic responses, providing sophisticated structures that mitigate challenges such as the harmful effects of urban noise pollution. However, vibroacoustic problems require distinct governing equations for air and structural subdomains, making standard density-based TO methods unsuitable. This challenge can be addressed by adopting a mixed displacement/pressure formulation, enabling unified modeling of air and structure. In this work, this formulation is applied only to a localized design subdomain to balance its high computational cost, while the remaining acoustic domain uses a conventional pressure-based approach. A three-material interpolation scheme is introduced to optimize designs with air, solid, and porous materials, and is applied to three case studies. Additionally, structural continuity and load-carrying capacity are ensured by incorporating a linear elasticity TO problem under realistic loading conditions, achieving robust, acoustically optimized designs. • The displacement/pressure mixed formulation is adopted to solve topology optimization in vibroacoustic problems. • The computational cost is reduced by combining this approach with the standard pressure formulation where applicable. • A three-material scheme is implemented using a two-variable RAMP interpolation model. • The resulting approach is applied to three case studies to mitigate noise emissions at target frequencies, and the results are discussed.