Lightweight integrated sound absorbing-insulating metamaterials with low thickness

doi:10.1007/s10483-026-3352-6

Abstract

Abstract:

This paper proposes two types of integrated sound absorbing-insulating metamaterials with low thickness and efficient sound attenuation in the low-frequency bandwidth, i.e., labyrinth-type metamaterial and multi-order resonator metamaterial. The labyrinth-type metamaterial is designed through spatial dimension transfer, transferring the required dimension in the thickness direction to the planar thin layer. Based on the Helmholtz resonance, the metamaterial achieves noise reduction through the reflection of sound waves and the thermoviscous dissipation of holes and cavities. This mechanism enables its sound insulation performance to produce the same gain effect as absorption, thereby accomplishing the broadband absorbing-insulating integrated design. With a thickness of only 33 mm, it achieves both sound absorption and insulation effects over more than one octave. The multi-order resonator metamaterial has a larger working bandwidth than the labyrinth-type metamaterial. It is designed based on the multi-order resonance absorption mechanism, and consists of 9 different orders of resonator units. The metamaterial obtains a continuous sound absorption coefficient curve in the low-frequency range of 362–1 712 Hz, and possesses high transmission loss (TL) above 346 Hz. In addition, this paper deeply explores the sound absorbing-insulating mechanism through the correlation analysis between the sound absorption coefficient and TL curves. The experimental results verify the continuous and efficient absorption effects of the two metamaterials, as well as their insulation performance that breaks the mass law. In low-frequency engineering applications, the two designed metamaterials demonstrate great potential and value at sub-wavelength dimensions.

Key words: acoustic metamaterial, low-frequency bandwidth noise reduction, integrated sound absorbing-insulating, Helmholtz resonance, thermoviscous dissipation, spatial folding

2010 MSC Number:

O422.4

Weidi XIA, Hongxing LI, Guotao ZHA, Fulin GUO, Chongrui LIU, Fuyin MA. Lightweight integrated sound absorbing-insulating metamaterials with low thickness. Applied Mathematics and Mechanics (English Edition), 2026, 47(2): 215-234.

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Figures/Tables 11

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Table 1

Performance comparison of typical noise reducing acoustic metamaterials"

Structural model	Working band	Absorption coefficient/TL	Thickness	Reference
Neck-embedded Helmholtz resonator	800–3 300 Hz	$A > 0.9$	About 40 mm	[33]
Cascade neck-embedded Helmholtz resonator	320–6 400 Hz	$A > 0.9$	100 mm	[45]
Multiscale porous material with coiled-up channel	213–3 000 Hz	$A > 0.7$	100 mm	[53]
Multiple-cavity metastructure with gradient thickness	315–1 326 Hz	$A > 0.7$	95 mm	[54]
Labyrinth-type integrated metamaterial	425–1 005 Hz	$A > 0.83$ $TL$ equals about 38 dB	33 mm	This work
Multi-order resonator integrated metamaterial	345–1 730 Hz	$A > 0.85$ $TL$ equals about 53 dB	82 mm	This work

Table 1

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