Dynamic Shaping of Multi-Touch Stimuli by Programmable Acoustic Metamaterial

TL;DR

This work addresses the rigidity of passive acoustic metamaterials by introducing dual-state unit cells built from off-the-shelf LRAs that switch between actuator and resonator modes to create a self-tuned, deep subwavelength band gap around $f_0\approx223\,\mathrm{Hz}$. The approach enables real-time wavefield shaping, localized vibrotactile patterns, and spatiotemporal encoding, demonstrated in a 1D prototype with rapid reconfiguration ($<25\,\mathrm{ms}$) and a practical bandwidth of about $120\,\mathrm{bits/s}$ at $50\,\mathrm{mm}$ spacing. Key results include robust band-gap formation with attenuation up to $-13.2\,\mathrm{dB}$, boundary-impedance invariance, and successful perceptual and path-following demonstrations (3-bit spatial messages and traveling vibration spots). The method offers a low-cost, turnkey platform for programmable vibrotactile displays and has potential for assistive haptics, mechanical computing, and scalable active metamaterials using consumer components, thereby broadening access to dynamic wave control. $$f_0=223\,\mathrm{Hz},\ \lambda/L\approx22,\ \text{band-gap range roughly }[160,290]\,\mathrm{Hz},\ \text{bandwidth }\approx120\,\mathrm{bits/s}.$$

Abstract

Acoustic metamaterials are artificial structures, often lattice of resonators, with unusual properties. They can be engineered to stop wave propagation in specific frequency bands. Once manufactured, their dispersive qualities remain invariant in time and space, limiting their practical use. Actively tuned arrangements have received growing interest to address this issue. Here, we introduce a new class of active metamaterial made from dual-state unit cells, either vibration sources when powered or passive resonators when left disconnected. They possess self-tuning capabilities, enabling deep subwavelength band gaps to automatically match the carrier signal of powered cells, typically around 200Hz. Swift electronic commutations between both states establish the basis for real-time reconfiguration of waveguides and shaping of vibration patterns. A series of experiments highlight how these tailored acceleration fields can spatially encode information relevant to human touch. This novel metamaterial can readily be made using off-the-shelf smartphone vibration motors, paving the way for a widespread adoption of multi-touch tactile displays.

Figures (5)

• Figure 1: Overview of the dual-state active acoustic metamaterial.A. Schematic of a 2D tactile display made from a square tessellation of dual-state unit cells. Cells in a resonator state (blank) form a metamaterial insulating cells in an actuator state (colored). The resulting vibration patterns can be reconfigured in real time. A reduced linear array of 11 unit cells is outlined in black. B. Equivalent electromechanical model given in both states: the "actuator state" and the "resonator state". Mechanical and electrical energy flux are overlaid (dissipative phenomena are discarded). C. Schematic of the linear array of 11 unit cells made with LRAs. D. Exploded view of an off-the-shelf LRA with, from top to bottom, a FR-4 substrate (SU), a voice coil (CL), a flexure spring (FL), a moving mass with a neodymium magnet (MM), and a steel casing (SC). E. Impulse response of a single LRA measured using a laser interferometer. Both the gain and phase, averaged over 50 trials, are well approximated by a second order model with minimal damping. F. Top view of the prototype with embedded electronics.
• Figure 2: Band gap analysis.A. Metamaterial as an infinite series of Timoshenko-Ehrenfest beams with effective springs, $K^*$ , attached to each junction, modeling the resonant action of LRAs. B. Dispersion graphs showing complete band gaps for different PCB thicknesses. Real and imaginary parts of the wave vector yield propagative and evanescent modes, respectively. C. Human vibrotactile threshold defined, at a given frequency, as the minimal peak-to-peak vibration amplitude perceivable. Reproduced from MountcastleEtAl-72BolanowskiEtAl-88. D. Left-hand side transmission coefficient with respect to the central unit cell, $n=6$. E. Transmission coefficient as a function of distance from the vibration source. F. Frequency shift of the attenuation peaks. G. Variations in transmission coefficients for $n=2$, where shades of blue and green represent increasing levels of flexure tension relative to the reference $\delta x=0mm$. H. Frequency-averaged variations in transmission coefficients as a function of distance from the vibration source.
• Figure 3: High-speed reconfiguration.A. Interpolated RMS acceleration field for two unit cells actuated. B. Schematic of the experiment with two unit cells driven by sine waves. C. Exponential increase in attenuation with the distance between sources. D. Maximum gradient of the acceleration field. The inflection point marks the transition from crosstalk between both sources to distinct vibration spots. E. Steady-state RMS acceleration with actuation of LRA $n=11$, then commuted to LRA $n=6$, for a 205Hz carrier. F. Rising and falling edges recorded during the electronic commutation of LRAs $n=6$ and $n=11$, respectively. The dotted line represents the exponential envelope of the LRA settling. G. Steady-state RMS acceleration for 3-bit binary numbers counted from zero to seven in 25ms intervals. H. Decoding sequence with binarization using thresholds optimized for each carrier. I. Decoding success rate as a function of the time delay between each word.
• Figure 4: Perceptual experiment.A. Confusion matrices from the perception of localized vibration patterns that encode binary representations of integers from one to seven. Results averaged across all participants. B. Average success rate of the matching task, either aggregated or categorized by the number of LRAs activated simultaneously. Error bars represent one standard deviation. The dashed line represents a chance threshold of 1/7.
• Figure 5: Wavefield guiding along spatiotemporal paths.A. Activation sequence of LRAs supplied with Slepian-windowed carrier signals. Up to five LRAs were activated simultaneously. B. Recorded acceleration field following a linear spatiotemporal reference path represented by the dashed line. C. Evolution of the vibration spot for various path speeds, and corresponding linear fits. D. Spatiotemporal vibration maps. The top row was obtained by bi-linear interpolation of the RMS acceleration, and the bottom row by Otsu's binarization. E. Sinusoidal reference path sweeping the metamaterial lengthwise at 3Hz. F. Metrics for assessing path-following effectiveness.