Anastasiia O. Krushynska –
Federico Bosia –
Nicola M. Pugno –
Laboratory of Bio-inspired and Graphene Nanomechanics
Department of Civil, Environmental and Mechanical Engineering
Uiversity of Trento
Via Mesiano 77
Trento, 38123, ITALY

Popular version of paper 1aNS3, “Fractal and bio-inspired labyrinthine acoustic metamaterials”
Presented Monday morning, May 7, 2018, 9:15-9:35, Nicolett 3D
175th ASA Meeting, Minneapolis

Road, rail, airports, industry, urban environments, crowds – all generate high-volume sound. When sound becomes uncomfortable or even painful to the ear, it is generally called noise. Nowadays, noise is one of the most widespread environmental problems in developed countries, negatively affecting public health and quality of life. Recent findings of the World Health Organization show that noise pollution is not only annoying for a large percentage of the population, but also causes sleep disturbance, increases the risk of cardiovascular diseases, intensifies the level of stress and hinders learning processes. Low-frequency noise is the most troublesome type and is mainly produced by road vehicles, aircraft, industrial machinery, wind turbines, compressors, air-conditioning units, etc.

The attenuation or elimination of low-frequency noise is a challenging task due to its numerous sources, its ability to bypass obstacles, and the limited efficiency of most sound barriers. The laws of acoustics tell us that if a solid wall is used to attenuate noise, sound transmission is inversely proportional to its mass per unit area and the sound frequency. This means that very heavy walls, more than ten meters thick (!), are necessary to efficiently reduce typical low-frequency noise in the frequency range between 10 and 1000 Hz.

Fortunately, modern technology can provide more 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 enhanced internal structural losses. The latter can be induced by incorporating internal resonators, which transfer mechanical vibrational energy into heat, or by using a geometry-related mechanism, exploiting the artificial elongation of sound propagation paths by means of narrow, so-called “labyrinthine” channels. In this work, we develop labyrinthine acoustic metamaterials with long narrow channels inspired by the structure of spider webs or arranged along fractal space-filling curves. These particular designs help to extend the metamaterial functionalities as compared to simpler configurations analyzed in previous years.

What happens if a sound wave enters a straight narrow channel? Depending on the channel geometry, it can either 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 happens if the channels are arranged in the shape of a maze or if there is a set of coiled channels? We now know that for certain configurations, other types of collective resonances can be induced – Mie resonances – that enable the achievement of total reflection at rather wide frequency ranges.

We have found out that natural spider-web designs for the channel labyrinths provide sufficient freedom for the development of metamaterials with switch on/off regimes between total transmission and total reflection that can be easily adapted for controlling low-frequency sound. In particular, we have shown that 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, we can tune operating frequencies to desired ranges. In fact, the proposed metamaterials provide exceptional versatility for application in low-frequency sound control and noise abatement.

Incorporation of more advanced designs, e.g. coiling wave paths along space-filling curves, enables to develop more compact configurations and opens a route for creating efficient sound absorbers [2]. Space-filling curves are lines constructed 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 [3]. This could be the next chapter to be written in the story of efficient noise abatement through innovative metamaterials.


[1] A.O. Krushynska, F. Bosia, M. Miniaci and N. M. Pugno, “Spider web-structured labyrinthine acoustic metamaterials for low-frequency sound control,” New J. Phys., vol. 19, pp. 105001, 2017.

[2] A.O. Krushynska, F. Bosia, and N. M. Pugno, “Labyrinthine acoustic metamaterials with space-coiling channels for low-frequency sounf control,” Acta Acust.united Ac., vol. 104, pp. 200–210, 2018.

[3] A.O. Krushynska, V. Romero-García, F. Bosia, N.M. Pugno, J.P. Groby, “Extra-thin metamaterials with space-coiling designs for perfect sound absorption”, (working paper), 2018.

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