Fixed in spatial distribution, arrays of planar, electromechanical acoustic transducers cannot adapt their wave energy focusing abilities unless each transducer is externally controlled, creating challenges for the implementation and portability of such beamforming systems. Recently, planar, origami-based structural tessellations are found to facilitate great versatility in system function and properties through kinematic folding. In this research we bridge the physics of acoustics and origami-based design to discover that the simple topological reconfigurations of a Miura-ori-based acoustic array yield many orders of magnitude worth of reversible change in wave energy focusing: a potential for acoustic field morphing easily obtained through deployable, tessellated architectures. Our experimental and theoretical studies directly translate the roles of folding the tessellated array to the adaptations in spectral and spatial wave propagation sensitivities for far field energy transmission. It is shown that kinematic folding rules and flat-foldable tessellated arrays collectively provide novel solutions to the long-standing challenges of conventional, electronically-steered acoustic beamformers. While our examples consider sound radiation from the foldable array in air, linear acoustic reciprocity dictates that the findings may inspire new innovations for acoustic receivers, e.g. adaptive sound absorbers and microphone arrays, as well as concepts that include water-borne waves.

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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.

Acoustic transducer arrays yield large spatial and spectral change in energy transmission through strategic positioning of planar array elements. Yet, unless array elements are actively tuned through phase delay controls, the array performance characteristics remain fixed and suitable for limited purposes. Origami, the art of paper folding, is a means to introduce enormous topological change through simple, kinematic translation and rotation of connected, planar facets, which is one reason for its growing attention as a fluent vehicle to remarkably adapt system properties for multifunctional purposes. In this research, we integrate acoustic transducer array development and origami design principles to establish a new framework for adaptive acoustic energy shaping effected by simple geometric and kinematic folding relations. From a flat-folded strip to an unfolded plane, our theoretical and experimental results show that this transducer design concept leads to powerful means to tune the significance of radiated acoustic energy across orders of magnitude and to easily tailor the acoustic power transmission to the far field.

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