[Paper Review] Exploiting Localized Transition Waves to Tune Sound Propagation in Soft Materials

Audrey A. Watkins, Austin Eichelberg+1 more|arXiv (Cornell University)|Sep 21, 2021

Advanced Materials and Mechanics38 references19 citations

TL;DR

This paper demonstrates that localized transition waves—driven by defect nucleation and propagation in compressed, frustrated soft lattices of levitated magnetic disks—can be harnessed to actively tune sound wave propagation. By exploiting instabilities and geometric frustration in systems with 1–4 magnets per disk, the authors show that time-independent, defect-mediated waves emerge under compression, enabling precise control over acoustic transmission, even in disordered configurations.

ABSTRACT

Programmable materials hold great potential for many applications such as deployable structures, soft robotics, and wave control, however, the presence of instability and disorder might hinder their utilization. Through a combination of analytical, numerical, and experimental analyses, we harness the interplay between instabilities, geometric frustration, and mechanical deformations to control the propagation of sound waves within self-assembled soft materials. We consider levitated magnetic disks confined by a magnetic boundary in-plane. The assemblies can be either ordered or disordered depending on the intrinsic disk symmetry. By applying an external load to the assembly, we observe the nucleation and propagation of different topological defects within the lattices. In the presence of instabilities, the defect propagation gives rise to time-independent localized transition waves. Surprisingly, in the presence of frustration, the applied load briefly introduces deformation-induced order to the material. By further deforming the lattices, new patterns emerge across all disk symmetries. We utilize these patterns to tune sound propagation through the material. Our findings could open new possibilities for designing exotic materials with potential applications ranging from sound control to soft robotics.

Motivation & Objective

• To investigate how instabilities and geometric frustration in self-assembled soft materials influence wave propagation.
• To explore whether deformation-induced defect dynamics can be used to actively tune acoustic properties in soft matter.
• To demonstrate that disordered, frustrated lattices can exhibit ordered wave transmission behavior through defect engineering.
• To validate the interplay between mechanical deformation, topological defects, and sound wave control through analytical, numerical, and experimental methods.

Proposed method

• Modeling infinite periodic lattices using Bloch’s theorem to derive dispersion relations for systems with 1–4 magnets per disk.
• Using the Verlet integration method to simulate time-evolving dynamics of finite lattices (10 disks) under controlled compression.
• Applying a chirp signal (0.2–10 Hz) to the rightmost disk to excite longitudinal waves and analyzing transmission via FFT.
• Measuring disk displacements experimentally using digital image correlation (DIC) on air-bearing levitated magnetic disks.
• Defining energy per unit cell (EUC) as a metric to identify defects: higher EUC indicates multiple disks per potential well.
• Modeling magnetic interactions via inverse power-law forces (f(d) = Ad^γ, γ = −4) and incorporating stiffness matrices dependent on wavenumber.

Experimental results

Research questions

• RQ1 Can defect nucleation and propagation in frustrated magnetic disk lattices be used to create tunable, time-independent transition waves?
• RQ2 How does mechanical compression induce transient order in disordered, frustrated lattices (e.g., three-magnet disks) and affect wave transmission?
• RQ3 To what extent do experimentally observed transmission spectra and dispersion curves match analytical and numerical predictions in both ordered and disordered systems?
• RQ4 Can the same defect-mediated wave control be achieved across different disk symmetries (1–4 magnets), and how do defect types vary with symmetry?

Key findings

• In disordered, three-magnet disk lattices (geometrically frustrated), compression induces transient order, enabling wave transmission that closely matches predictions for perfectly ordered lattices.
• Numerical and experimental transmission spectra for all disk types (1–4 magnets) show strong agreement, with transmission bands increasing in frequency as the number of magnets per disk increases.
• A distinct transmission anomaly near 1 Hz emerges in both simulations and experiments in frustrated lattices but dissipates with distance due to increasing disorder.
• Defects propagate as time-independent localized transition waves: one- and two-magnet systems exhibit two-disk defects, while four-magnet systems form three-disk defects under compression.
• Energy per unit cell (EUC) analysis confirms defect presence: elevated EUC values correlate with multiple disks per potential well and phase-angle transitions.
• In 50-disk lattices, defect propagation remains stable and identifiable over long distances, confirming the robustness of the transition wave mechanism beyond edge effects.