Topology Optimization of Acoustic-Poroelastic-Elastic Structures for Sound Attenuation

Abstract

Structures for sound attenuation have been explored in many scenarios, ranging from civil construction to automotive and aerospace industries. However, the proper multiphysics interactions of acoustic-poroelastic-elastic structures are still challenging, especially when topology optimization techniques are involved. This work entails a new topology optimization methodology based on the Bidirectional Evolutionary Structural Optimization (BESO) approach to design bidimensional structures for sound attenuation enhancements. The full modeling of poroelastic bodies is done by the mixedu/p technique. At the same time, the elastic and acoustic (air) materials are obtained by the degeneration of the latter, leading to the well-known elasto-dynamic and Helmholtz formulations, respectively. Such procedure is done in by the combination of the Finite Element Method (FEM) with the Unified Multiphase (UMP) modeling approach, which in turn contributes to the development of material interpolation schemes suited for the application. In this scenario, the topology optimization problem is established as the maximization of the time-averaged dissipative power, composed by the summation of its structural, viscous and thermal dissipative components. The numerical examples show the effectiveness of the proposed methodology since it provides well-defined topologies with generally enhanced dissipative performances.

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