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

Abstract

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.

Miura-ori enabled stretchable circuit boards

“…Origami is an ancient form of papercraft in which, following predesigned patterns, two-dimensional sheets are folded into compact and deformable three-dimensional structures 17 . A widely recognized origami form, Miura fold (or Miura-ori), which has various desired properties, including stretchability and rigid foldability, has been used in engineering, architecture, and artistic design [17][18][19][20] . The strain is effectively suppressed in the rigid facet areas with the deformation mainly localized on the creases, making the Miura-ori compatible with rigid or nonflexible components 21,22 .…”

Acoustic wave focusing by doubly curved origami-inspired arrays

“…For instance, tessellated water-bomb and star-based arrays of acoustic transducers studied by Lynd et al (2017) and Zou et al (2018) have wave guiding properties in the near and far field in addition to the ability to fold into compact shapes for transport. Moreover, the reconfiguration of such origami-inspired acoustic arrays empowers means to control interference phenomena and thus modulate the wave guiding properties (Lynd and Harne, 2017; Zou et al, 2018; Zou and Harne, 2017, 2018).…”

Adaptive acoustic energy delivery to near and far fields using foldable, tessellated star transducers

“…Building upon this inspiring framework of engineering design, the authors have recently introduced a concept of acoustic beamfolding, wherein the tessellated surfaces of the Miura-ori origami fold pattern serve as the substrate for acoustic transducers [35,36]. Acoustic beamfolding therefore is a class of MSP that guides sound energy via the topological reconfiguration of the foldable Miura-ori-inspired arrays.…”

“…Contrasting this attention, when deploying ultrasonic waves, such as for medical diagnostics and treatment, a common need is to focus acoustic energy at strategic points in space, often in the near field of the transducers and arrays. In this perspective, the analysis put forward in the previous works [35,36] is applicable only for the prediction of sound pressure radiation to points in the acoustic far field. Therefore, a modeling methodology able to characterize both near and far field acoustic energy delivery from tessellated acoustic transducers is needed to begin uncovering opportunities for a more generalized guiding of acoustic energy via foldable, tessellated transducers.…”

“…The unfolded square shape of the Star transforms into three-dimensions by folding, although the tessellation is not flat foldable. Along with the focus on this new constituent comes the opportunity to establish new analytical procedures that facilitate prediction of near field sound energy delivery, which was not previously undertaken [35,36].…”