Strategies to predict radiated sound fields from foldable, Miura-ori-based transducers for acoustic beamfolding

To bypass challenges of digital signal processing for acoustic beamforming applications, it is desirable to investigate repeatable mechanical approaches that accurately reposition transducers for real-time, simple guiding of acoustic energy. One promising approach is to create arrays configured on origami-inspired tessellated architectures. The low dimensionality, easy implementation, compactness, and use of straightforward folding to guide acoustic energies suggest that tessellated arrays may bypass limitations of conventional digital signal processing for beamforming. On the other hand, the challenge of developing such reconfigurable arrays lies in determining tessellation design and folding extent that direct sound as required. This research assesses the utility of the computationally efficient, approximate solutions to Rayleigh's integral to predict radiated sound fields from tessellated arrays based on Miura-ori fold patterns. Despite altering assumptions upon which the integral is derived, it is found that the salient beam-steering properties and amplitudes are accurately reconstructed by the analytical approach, when compared to boundary element model results. Within the far field angular space accommodated by the formulation assumptions, the analytical approach provides a powerful, time-efficient, and intuitive means to identify tessellated topologies and folding extents that empower desired wave-guiding functionalities, giving fuel to the concept of acoustic beamfolding.