Advancing Boundary Dependent Topology Optimization: Towards Optimal Viscothermal Vibroacoustic Structures

The performance and miniaturization demands of modern vibroacoustic devices, such as hearing aids, present significant design challenges due to complex boundary interactions and strongly coupled multiphysics phenomena. These intricacies make traditional trial-and-error approaches both time-consuming and impractical, highlighting the need for advanced computational optimization techniques. This thesis addresses these challenges through topology optimization, a method that facilitates broad exploration of spatial design configurations and enables the discovery of novel, high-performing vibroacoustic structures.

The primary objective of this work is to advance topology optimization methodologies tailored to vibroacoustic systems governed by strongly coupled structural and acoustic physics, with particular emphasis on modeling viscothermal boundary losses. This marks a foundational step toward a physically comprehensive optimization framework capable of capturing the full complexity of real-world vibroacoustic devices.

To this end, the thesis introduces novel multiphysics interpolation schemes designed to overcome critical challenges in strongly coupled vibroacoustic topology optimization. In addition, a boundary interpolation framework is developed, enabling the imposition of arbitrary boundary conditions and transforming conventional topology optimization into a boundary-aware design tool. As a compelling demonstration of the developed methods, the thesis presents the design of a viscothermal vibroacoustic black hole—an advanced concept that illustrates the flexibility and effectiveness of the proposed framework. Collectively, these contributions pave the way for high-fidelity, computationally optimization of next-generation vibroacoustic devices, including hearing aids and other complex multiphysics systems.