Design optimization of phononic-fluidic resonator systems

Phononic-fluidic resonators utilize an acoustic fluid domain as a defect inside a solid metamaterial lattice, which can be used used to precisely measure acoustic properties of liquids. The design goal is to offer ideal boundary conditions for the acoustic resonator by matching defect resonance with phononic band gap. The design space of metamaterial or phononic crystal and fluidic resonator is nearly unlimited, especially when utilizing fully three-dimensional structures. In this work, we explore numerical shape and topology optimization to focus acoustic energy into the fluid domain and maximize the quality factor of the defect resonance. This requires the use of complex multi-frequency objective functions, while taking into account practical limits such as finite size and losses in the fluid and solid domains. Results highlight notable but limited improvements of quality factor with shape optimization starting from an initial design constrained by the maximum deformation possible. On the other hand, topology optimization results offer unique and unexpected ideas, and thus a deeper dive into the design space.