Topology optimization for vibroacoustic problems

Topology optimization is a powerful, versatile tool that has been applied successfully in many engineering fields. In vibro-acoustic design problems, the fact that the interface between the solid and the acoustic domains varies during the optimization poses an extra challenge for the sensitivity calculation. In this paper, two topology optimization methods for structure-acoustic interaction problems that have been proposed in the literature are compared in the context of hearing aid suspension design, a system where the structural-acoustic coupling is strong due to the suspension shape and material properties. The first method, referred to as "Mixed-MMA", uses a mixed formulation of the fluid-structure interaction problem where both the structural and the acoustic domains are governed by the same equations and present displacement and pressure primary variables. This allows for converting solid elements into fluid ones, and vice-versa, by varying their material properties, which can be done in a smooth way by allowing intermediate elements during the optimization. The second method, referred to as "Segregated-BESO", uses the more conventional formulation of the problem where the solid and the acoustic domains are described by different equations and primary variables; therefore, the fluid-structure interface must be well-defined at all stages, and an optimization strategy that uses discrete variables is used. A drawback of the second method is that the sensitivities cannot be calculated accurately, since an interpolation scheme between solid and acoustic elements is not available; however, attractive features are the ease of implementation in commercial FE softwares and the compactness of the segregated formulation. The performance of the two methods is evaluated on a 2D suspension design problem for different degrees of the structure-acoustic coupling strength, which shows that the Segregated-BESO method is challenged due to the sensitivity errors when the coupling is strong.