Vibro-acoustic shape optimization for radiation problems: Application to compact loudspeakers

Shape optimization is a promising tool for improving and guiding the design of computationally large-sized vibro-acoustic devices such as compact loudspeaker systems and hearing aids. Typically, such devices are subject to unwanted structural vibrations that can degrade the acoustic performance, i.e., contributing with destructive and constructive interference or creating feedback problems. Numerical-based shape optimization can potentially help engineers to limit or control these vibrational effects. This work presents i) a method to perform gradient-based vibro-acoustic shape optimization and ii) an investigation of the impact of different cost function formulations. The shape optimization framework is based on a coupled vibro-acoustic Finite Element and Boundary Element utilizing a Free Form Deformation parametrization approach. The framework will be used to control the acoustic radiation characteristics of vibrating structures, having the design of compact loudspeakers in mind. When performing shape optimization, a difficult task is to formulate appropriate cost functions that can create well-performing designs in a broadband frequency range. Therefore, the work will discuss different cost function definitions, mainly focusing on manipulating the directivity performance of the acoustic radiation from vibrating structures.