The urban environment produces high-volume sound, which is often called noise. Nowadays, noise is a widespread environmental problem in many countries, which negatively affects public health and quality of life. Low-frequency noise is of the most troublesome type due to its numerous sources, its ability to bypass obstacles, and the limited efficiency of most sound barriers. To efficiently attenuate low-frequency noise of frequencies between 10 and 1000 Hz, we need thick walls, up to ten meters of thickness (!).

Fortunately, modern technology can provide innovative and efficient solutions, based on so-called acoustic metamaterials. These are engineered structures capable of effectively slowing down sound speed and reducing sound intensity thanks to internal structural losses. The latter can be induced, e.g., by means of a geometry-related mechanism based on an artificial elongation of sound propagation paths in narrow “labyrinthine” channels. In this research, we develop labyrinthine acoustic metamaterials with long channels inspired by the structure of natural spider webs [1] or fractal space-filling curves [2]. These particular designs help to extend the metamaterial functionalities as compared to simpler configurations analyzed in previous years (More details at acoustics.org).

This research has been done in collaboration with Dr. F. Bosia from University of Turin, Italy, and Prof. N.M. Pugno from University of Trento, Italy.

References

1. Krushynska A.O., Bosia F., Miniaci M., Pugno N.M. “Spider-web structured labyrinthine acoustic metamaterials for low-frequency sound control”, New J. Phys. 19, 105001, 2017 (link).
2. Krushynska A.O., Bosia F., Pugno N.M. "Labyrinthine acoustic metamaterials with space-coiling channels for low-frequency sound control", Acta Acust. united Acustica 104, 200-210, 2018 (link).

Physics of labyrinthine channels

What happens if a sound wave enters a straight channel? Depending on the channel width, it can either freely propagate through it or be attenuated. For narrow channels, friction effects in the vicinity of the channel walls hinder wave propagation and can eventually lead to its total attenuation. For moderately wide channels, if the sound wavelength matches the distance between the two channel edges (i.e., it equals an integer number of half wavelengths), resonance takes place, allowing to amplify the sound transmission. Both the described effects take place at single frequencies.

But what if channels are arranged in the shape of a maze or as a set of coiled channels? For certain configurations, several collective resonances can be induced – Mie resonances – that enable the achievement of total reflection at rather wide frequency ranges.

We have shown that spider-web designs for the channel labyrinths provide sufficient freedom for the development of acoustic metamaterials with switch on/off regimes between total transmission and total reflection, and can be easily adapted to control low-frequency sound. In particular, a light-weight re-configurable structure with a square cross section of 0.81 m² is capable of totally reflecting airborne sound at frequencies of 50-100 Hz and above [1]. Moreover, by modifying the channel thickness and length, operating frequencies can be tuned to desired ranges. In fact, the proposed metamaterials provide exceptional versatility for application in low-frequency sound control and noise abatement.

More advanced designs, e.g. coiling wave paths along space-filling curves, results in compact metamaterial configurations and opens a route for the development of efficient sound absorbers [2]. Space-filling curves are lines constructred by an infinite iterative process with the aim to fill in a certain area, e.g. a square or cube. Since the work of G. Peano (1890) until the 1980s, these curves were considered no more than mathematical curiosities, and only recently have they found application in fields like data science and routing systems. The use of space-filling curves for wave path labyrinths in combination with the added effect of friction in narrow channels has allowed us to achieve total reflection or to improve wave absorption of low-frequency sound. The absorption can be increased up to 100 % at selected frequencies, if a hybrid configuration with incorporated Helmholtz resonators is used. This could be the next chapter to be written in the story of efficient noise abatement through innovative metamaterials.

References

1. Krushynska A., Bosia F., Miniaci M., Pugno N.M. “Spider-web structured labyrinthine acoustic metamaterials for low-frequency sound control”, New J. Phys. 19, 105001, 2017 (link).
2. Krushynska A.O., Bosia F., Pugno N.M. "Labyrinthine acoustic metamaterials with space-coiling channels for low-frequency sound control", Acta Acust. united Acustica 104, 200-210, 2018 (link).
3. Krushynska A.O., Romero-Garcia V., Bosia F., Pugno N.M., Groby J.-P. "Perfect absorption and total reflection in space-coiled sub-wavelength channels", 12th International Congress on Engineered Materials Platforms for Novel Wave Phenomena (Metamaterials): Espoo, Finland, p.240-242.