Bending waves focusing in arbitrary shaped plate-like structures: Application to spatial audio in cars

Abstract

Advanced automotive audio applications are more and more demanding with respect to the visual impact of loudspeakers while still requiring more and more channels for high quality spatial sound rendering. The use of arbitrary plate-like structures driven by electromagnetic actuators or by piezoelectric elements appears as a promising solution to tackle both issues. However, to meet spatial rendering audio constraints (i.e. to be as close as possible to omnidirectional piston-like sources), the generated bending waves must be focused at a given position and to a certain extent within the host plate which can be of arbitrary shape, material, and thickness. Theoretically, this means being able to invert the spatio-temporal wave propagation operator for the generated bending waves to fit a given target shape. There are several methods (modal control, time-reversal, and propagating waves operator inversion) that allow to focus bending waves in a media. However, there is scarce work on their adaption and performances assessment in the context of audio applications. These methods depend differently on the available knowledge of wave propagation in the plate (theoretical, partial spatial or full spatial knowledge) and are here investigated to perform this task. Their performances are assessed with respect to several aspects: geometrical complexity, thickness, and material damping of the host structure, number and type of actuators, position and extent of the focusing area. The various methods are presented in a unified theoretical framework and they are compared by means of two key performance indexes (focus localization error and spatial contrast). An experimental validation on a relevant industrial case is also carried out and learning through a digital twin instead of time consuming experimental data investigated. This work falls within the framework of research which tries to bridge the gap between laboratory research and industrial deployment of this kind of technologies.