A sound absorption panel containing coiled Helmholtz resonators
Introduction
The last decade has witnessed a growing interest in the study of low-frequency sound absorption. Conventionally, sound absorption took advantages of porous/fibrous materials or objects with gradient index. The above-mentioned subjects usually work well at high frequencies, but they work inefficiently at low frequencies [1], [2], [3], [4], [5]. The use of resonant structures, such as locally resonant sonic crystals [6], [7], decorated membrane resonators [8], [9], [10], split tube resonators [11], [12], micro-perforated panels [13], [14], [15], and Helmholtz resonators (HRs) with spiral or extended necks [16], [17], [18], [19], [20], [21], [22], provides an additional possibility for low-frequency sound absorption. Although HRs with spiral or extended necks can effectively lower their working frequency, they are rarely installed in a compact space, especially for thin panels. Recently, the concept of coiling up space has been applied to the manipulation of acoustic waves [23], [24], [25], [26], [27], [28], [29]. Extraordinary dispersion, including negative refraction and conical dispersion, has been found in those labyrinthine metamaterials. Another illustrative space-coiling example is acoustic metasurfaces. They usually consist of curled and one-end-closed channels [30], [31]. Thickness of this structure is subwavelength. An acoustic metasurface is able to tune its absorption bandwidth using the cross-sectional area of channel. To lower the operating frequency without increasing the total channel length, nonuniform or gradient cross sections were adopted [32], [33]. Other designs, such as multicoiled structures [34] or underdamped coiled space resonators covered by a surface sponge coating [35], can lead to nearly-perfect absorption. Alternatives of acoustic metasurfaces are to embed acoustic resonators with a classical, spiral, or folded cavity in perforated or microperforated plates [36], [37], [38], [39], [40]. Studies have shown that within a compact space, a space-coiling resonator is more efficient in reducing working frequency and improving sound absorption performance than conventional ones. In addition to attempting to establish the governing principles, the development of computational techniques to predict results has aroused much research interest [39], [40], [41].
Inspired by previous works, we propose a relatively simple structure, which still exhibits sound absorption capability in the low frequency regime. Instead of using complex geometry for cavities [40], the inner resonator is comprised of a small tube and a large tube in series. Both tubes are coiled up to fit the limited space. The small-sized tube can be viewed as the neck of resonator, while the large-sized one serves as the cavity. The operating frequency can be approximately estimated using the traditional formula for a Helmholtz resonator [42]. An analytical model is presented to predict sound absorption profile of the present structure. Theoretical predictions on absorption characteristics are verified by comparing those with simulation and experimental results. To effectively broaden the absorption bandwidth, a panel with double resonators arranged in parallel is introduced. The air velocity field associated with the maximum sound absorption is also examined in modeling.
Section snippets
Design model
Fig. 1(a) shows the proposed sound absorbing panel which consists of a thin covering board with a square hole, a main panel having two tubes of different sizes in series, and a back wall. For saving space, each tube is bent up. The large tube has three nearly turns; the small tube has one sharp and one moderate turns. The round turns at the corner of cavity are for maximized usage of space and consistency of the cross-sectional area. Though the cross-section of both tubes is square,
Single resonator
In the finite element (FE) analysis, commercial software COMSOL Multiphysics is utilized to conduct numerical simulations. The Acoustic Module is adopted in the computation. The simulated model is comprised of two tubes of different sizes connected in series. The small-sized and large-sized tubes can be viewed as the neck and cavity of a Helmholtz resonator, respectively. In the resonator region, boundary layer effects including viscous and thermal losses are considered. An oscillation sound
Conclusions
This study investigates the sound absorption performance of a panel containing coiled Helmholtz resonators. The compact structure is able to absorb low-frequency sound energy. The absorption peak frequency can be precisely predicted employing the concept of acoustic impedance. Analytical and numerical predictions agree well with experimental results. The peak frequency can be tailored by dimensions of tubes. When two resonators with different dimensions are exploited, dual absorption peaks can
CRediT authorship contribution statement
Jung-San Chen: Conceptualization, Funding acquisition, Methodology, Resources, Supervision, Writing - original draft. Yu-Bin Chen: Funding acquisition, Visualization, Writing - review & editing. Yu-Hsiang Cheng: Investigation, Software. Li-Chih Chou: Validation, Visualization.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by the Ministry of Science and Technology (MOST), Taiwan, under grant numbers MOST 106-2221-E-006-122-MY3 and 106-2628-E-007-006-MY3.
References (45)
Sound absorption in flexible porous materials
J. Sound Vib.
(1978)- et al.
Design optimization of porous fibrous material for maximizing absorption of sounds under set frequency bands
Appl. Acoust.
(2014) - et al.
Sound absorption of a finite flexible micro-perforated panel backed by an air cavity
J. Sound Vib.
(2005) - et al.
Helmholtz resonator with a spiral neck
Appl. Acoust.
(2015) - et al.
An extended neck versus a spiral neck of the Helmholtz resonator
Appl. Acoust.
(2017) - et al.
Effect of extended necks on transmission loss performances of Helmholtz resonators in presence of a grazing flow
Aerosp. Sci. Technol.
(2018) - et al.
Recent trends in porous sound-absorbing materials
Sound Vib.
(2010) - et al.
Light propagation with phase discontinuities: generalized laws of reflection and refraction
Science
(2011) - et al.
Metaporous layer to overcome the thickness constraint for broadband sound absorption
J. Appl. Phys.
(2015) - et al.
Locally resonant sonic materials
Science
(2000)
Matryoshka locally resonant sonic crystal
J. Acoust. Soc. Am.
Dark acoustic metamaterials as super absorbers for low-frequency sound
Nat. Commun.
Coupled decorated membrane resonators with large Willis coupling
Phys. Rev. Appl.
Bandwidth broadening for transmission loss of acoustic waves using coupled membrane-ring structure
Mater. Res. Express
Multilayer-split-tube resonators with low-frequency band gaps in phononic crystals
J. Appl. Phys.
Low-frequency tunable acoustic absorber based on split tube resonators
Appl. Phys. Lett.
Potential of microperforated panel absorber
J. Acoust. Soc. Am.
Micro-perforated structures as sound absorbers - a review and outlook
Acta Acust. Acust.
Helmholtz resonator with extended neck
J. Acoust. Soc. Am.
Manipulating reflected acoustic wave via Helmholtz resonators with varying-length extended necks
J. Appl. Phys.
Interferences in locally resonant sonic metamaterials formed from Helmholtz resonators
Appl. Phys. Lett.
A Helmholtz resonator with spiral neck for analyte concentration measurement in low frequency range
Appl. Sci.
Cited by (43)
Ultrathin arch-like labyrinthine acoustic metasurface for low-frequency sound absorption
2023, Applied Acoustics