Three dimensional vibroacoustic topology optimization of hearing instruments using cut elements

The focus of this article is on level set based topology optimization of vibroacoustic hearing instruments. The goal is to demonstrate the applicability of the proposed framework for optimization of 3D industrial scale hearing instruments. The framework employs an immersed boundary cut element method to handle the modeling of complex design geometries on fixed unstructured meshes. Utilization of unstructured meshes allows for optimizing small parts of a complex hearing instrument without disturbing the overall geometry. The remaining parts of the model which are not included in the optimization process are modeled with segregated approach. The design parameterization is based on an explicit level set approach, for which the nodal level set values are linked to the mathematical design variables. The optimization problem is solved using mathematical programming and the sensitivities are obtained with a discrete adjoint approach. A validation study is carried out comparing the proposed cut element model to a body fitted mesh for a large range of frequencies. The optimization framework is then applied on the tube and the suspension structures of a hearing instrument system considering two sets of material properties for the design parts. The optimization considers the minimization of sound pressure on the microphone surface for discrete frequencies aiming to reduce the feedback paths and to increase the amplification that the device can deliver to the user. Both optimization cases improve the performance of the hearing instrument system by effectively reducing the sound pressure on the microphone surface for the considered frequency range.