Researchers use LEGOs to decode intricate vibration patterns in quasi-crystalline matter

Some dynamics and topological principles in materials transcend systems of different sizes and mediums. The physics of topological insulators has inspired physicists to look into the possibility of designing metamaterials with tunable wave localization and transport properties, such as locally resonant metastructures.

Rosa et al. constructed an analog using LEGO pieces as an elastic model for studying a locally resonant metastructure. The setup consisted of a long LEGO strip with a single array of 42 pillar-cones attached to it. Each cone on the pillars, adjustable by their positions on the pillars, acts as a tunable resonating attachment to fulfill a quasi-periodic modulation law.

The contraption was attached to an electrodynamics shaker, which drove vibrations along the array. Data was collected using a scanning laser doppler vibrometer to produce resonant spectra resembling a Hofstadter’s butterfly. For the most part, their experimental observations resembled the theoretical prediction, other than a few discrepancies attributed to imperfections in the physical setup.

“While we had good numerical results, we were really surprised to find how such a simple experimental setup could capture the predicted behavior and produce a well-defined Hofstadter-like spectrum,” said author Matheus Rosa.

By tweaking the cone positions, they were able to control topological edge states that can be localized at either edges of the sample depending on a parameter of the modulation.

The success of using the LEGO setup to explore topological properties of 1D systems means it can be used to help design tunable devices, such as electromechanical waveguides. The authors plan to expand the LEGO method to study 2D systems, which may help explore higher dimensional topologies such as the 4D quantum Hall effect.

Source: “Exploring topology of 1D quasiperiodic metastructures through modulated LEGO resonators,” by Matheus I. N. Rosa, Yuning Guo, and Massimo Ruzzene, Applied Physics Letters (2021). The article can be accessed at https://doi.org/10.1063/5.0042294 .

This paper is part of the Metastructures: From Physics to Application special collection, learn more here .