Multi-material topology optimization of vibro-acoustic structures with acoustic, poroelastic and elastic media under mass constraint

Single-material topology optimization designs struggle to achieve the free selection of multiple materials in vibro-acoustic structures while adhering to budgetary and spatial constraints to obtain optimal objective performance. To address this challenge, this paper proposes a novel topology optimization approach tailored for multi-material vibro-acoustic structures based on the multi-material floating projection topology optimization (FPTO) method, which offers flexibility in adjusting the proportions of various materials, including acoustic, poroelastic, and elastic media, in the final optimized design. The mixed displacement/pressure (u/p) formulation based on Biot's theory and the linear multi-material interpolation model are used to overcome the potential difficulties in numerical analysis and topology optimization, and validated by the impedance tube test. The multi-material design variables are directly established on the volume fractions of multiple materials within each element and their 0/1 constraints are simulated by the multiple floating projection constraints. The proposed vibro-acoustic multi-material FPTO method is applied to minimize dynamic compliance or maximize sound transmission loss (STL) under a single mass constraint or multiple volume constraints. Some 2D and 3D benchmark numerical examples confirm that the optimized designs under a single mass constraint outperform those with multiple volume constraints and conventional designs. The presented results offer some valuable insights into multi-physics topology optimization and build a foundation for the design of composite engineering structures in vibration reduction and noise attenuation.