Open acoustic barriers exhibit excellent sound transmission reduction property at a certain frequency/frequencies which highly depends on the configuration of its unit cell. Design of unit cell configuration for minimum sound transmission at predefined objective frequency remains an open question. This paper aims at providing an automatic design method for open acoustic barriers with multi-material unit cell. Firstly, a wave finite element method is developed to calculate the sound transmission through an infinite array of periodic scatterers. As the unit cell contains infinite fluid domain, the application of Floquet-Bloch theorem to the boundaries of perfectly match layers (PML) is necessary and has been resolved in this paper. This wave finite element method with the implementation of PML is validated by comparing to analytical solution of sound transmission through an array of steel cylinders. Then a genetic algorithm is employed to optimize the sound transmission loss with respect to material distribution of a bi-material unit cell. Finally, the effectiveness of this inverse design is demonstrated by examples with different predefined frequencies. Corresponding unit cell typologies are obtained and the dips of sound power transmission coefficient curve are successfully tuned to objective frequencies.
HuangJShiZ.Attenuation zones of periodic pile barriers and its application in vibration reduction for plane waves. J Sound Vibrat2013; 332: 4423–4439.
2.
HuangJShiZ.Vibration reduction of plane waves using periodic in-filled pile barriers. J Geotech Geoenviron Eng2015; 141: 04015018.
3.
ShiZWenYMengQ.Propagation attenuation of plane waves in saturated soil by pile barriers. Int J Geomech2017; 17: 04017053.
4.
AchaouiYAntonakakisTBruleS, et al. Clamped seismic metamaterials: ultra-low frequency stop bands. New J Phys2017; 19: 063022.
5.
BrûléSEnochSGuenneauS, et al. Seismic metamaterials: controlling surface Rayleigh waves using analogies with electromagnetic metamaterials. Handbook of metamaterials. Singapore: World Scientific, 2018.
6.
Peiró-TorresMRedondoJBravoJ, et al. Open noise barriers based on sonic crystals. Advances in noise control in transport infrastructures. Transport Res Proc2016; 18: 392–398.
7.
RubioCCastiñeira-IbáñezSUrisA, et al. Numerical simulation and laboratory measurements on an open tunable acoustic barrier. Appl Acoust2018; 141: 144–150.
8.
DongHWSuXXWangYS, et al. Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm. Struct Multidisc Optim2014; 50: 593–604.
9.
DongHWSuXXWangYS, et al. Topology optimization of two-dimensional asymmetrical phononic crystals. Phys Lett A2014; 378: 434–441.
10.
XieLXiaBLiuJ, et al. An improved fast plane wave expansion method for topology optimization of phononic crystals. Int J Mech Sci2017; 120: 171–181.
11.
D, Hw S and Xx W. Ys. Topology optimization of two-dimensional phononic crystals using fem and genetic algorithm. In: 2012Symposium on Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA). Piscataway, NJ: IEEE, pp. 45–48.
12.
Li Y, Huang X, Meng F, et al. Topology optimization of 2d phononic band gap crystals based on Beso methods, advances in structural and multidisciplinary optimization. In: Proceedings 11th world congress of structural and multidisciplinary optimization (Qing L, Grant PS and Zhongpu (Leo) Z, eds), International Society for Structural and Multidisciplinary Optimization (ISSMO), Sydney, Australia, 7--12 June 2015, pp. 157--161. (ISBN 13: 978-0-646-94394-7)
13.
KookJJensenJS.Topology optimization of periodic microstructures for enhanced loss factor using acoustic–structure interaction. Int J Solids Struct2017; 122-123: 59–68.
14.
ChenYGuoDLiYF, et al. Maximizing wave attenuation in viscoelastic phononic crystals by topology optimization. Ultrasonics2019; 94: 419–429.
15.
LiYFMengFZhouS, et al. Broadband all-angle negative refraction by optimized phononic crystals. Sci Rep2017; 7: 7445.
16.
MengHWenJZhaoH, et al. Optimization of locally resonant acoustic metamaterials on underwater sound absorption characteristics. J Sound Vibrat2012; 331: 4406–4416.
17.
HuangLXiaoYWenJ, et al. Optimization of decoupling performance of underwater acoustic coating with cavities via equivalent fluid model. J Sound Vibrat2018; 426: 244–257.
18.
KristiansenUFahyF.Scattering of acoustic waves by an n-layer periodic grating. J Sound Vibrat1972; 24: 315–335.
19.
TwerskyV.On the scatttering of waves by an infinite grating. IRE Trans Antennas Propag1956; 4: 330–345.
20.
AudolyCDumeryG.Etude d’écrans sous-marins constitués de réseaux de tubes élastiques. Acta Acust United Acust1989; 69: 263–269.
21.
AudolyC.Diffraction d’une onde plane par un reseau de tubes compliants. Acustica1987; 64: 159–168.
BrighamGALibuhaJJRadlinskiRP.Analysis of scattering from large planar gratings of compliant cylindrical shells. J Acoust Soc Am1977; 61: 48–59.
24.
LynottGMAndrewVAbrahamsID, et al. Acoustic scattering from a one-dimensional array; tail-end asymptotics for efficient evaluation of the quasi-periodic green’s function. Wave Motion2019; 89: 232–244.
25.
HennionABossutRDecarpignyJ, et al. Analysis of the scattering of a plane acoustic wave by a periodic elastic structure using the finite element method: application to compliant tube gratings. J Acoust Soc Am1990; 87: 1861–1870.
26.
BerengerJP.A perfectly matched layer for the absorption of electromagnetic waves. J Comput Phys1994; 114: 185–200.
27.
BasuUChopraAK.Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation. Comput Meth Appl Mech Eng2003; 192: 1337–1375.
28.
JosifovskiJ.Analysis of wave propagation and soil–structure interaction using a perfectly matched layer model. Soil Dynam Earthquake Eng2016; 81: 1–13.
29.
FontaraIKSchepersWSavidisS, et al. Finite element implementation of efficient absorbing layers for time harmonic elastodynamics of unbounded domains. Soil Dynam Earthquake Eng2018; 114: 625–638.
30.
HarariISlavutinMTurkelE.Analytical and numerical studies of a finite element PML for the Helmholtz equation. J Comp Acous2000; 8: 121–137.
31.
BermúdezAHervella-NietoLPrietoA, et al. An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems. J Comput Phys2007; 223: 469–488.
32.
BaccoucheRTaharMBMoreauS.Perfectly matched layer for Galbrun’s aeroacoustic equation in a cylindrical coordinates system with an axial and a swirling steady mean flow. Journal of Sound and Vibration2016; 378: 124–143.
33.
FengXBen TaharMBaccoucheR.The aero-acoustic Galbrun equation in the time domain with perfectly matched layer boundary conditions. J Acoust Soc Am2016; 139: 320–331.
34.
BasuU. Perfectly matched layers for acoustic and elastic waves. Dam Safety Research Program, US Department of the Interior,2008.
35.
Hladky-HennionACDecarpignyJN.Analysis of the scattering of a plane acoustic wave by a doubly periodic structure using the finite element method: application to Alberich anechoic coatings. J Acoust Soc Am1991; 90: 3356–3367.
36.
WenJZhaoHLvL, et al. Effects of locally resonant modes on underwater sound absorption in viscoelastic materials. J Acoust Soc Am2011; 130: 1201–1208.
37.
MengHWenJZhaoH, et al. Analysis of absorption performances of anechoic layers with steel plate backing. J Acoust Soc Am2012; 132: 69–75.
38.
ShiKJinGLiuR, et al. Underwater sound absorption performance of acoustic metamaterials with multilayered locally resonant scatterers. Results Phys2019; 12: 132–142.
39.
RemillieuxMCBurdissoRA.Vibro-acoustic response of an infinite, rib-stiffened, thick-plate assembly using finite-element analysis. J Acoust Soc Am2012; 132: EL36–EL42.
40.
SigmundO.A 99 line topology optimization code written in matlab. Struct Multidisc Optim2001; 21: 120–127.
41.
AndreassenEClausenASchevenelsM, et al. Efficient topology optimization in Matlab using 88 lines of code. Struct Multidisc Optim2011; 43: 1–16.
42.
DeatonJDGrandhiRV.A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidisc Optim2014; 49: 1–38.
43.
Castiñeira-IbáñezSRubioCRomero-GarcíaV, et al. Design, manufacture and characterization of an acoustic barrier made of multi-phenomena cylindrical scatterers arranged in a fractal-based geometry. Archives of Acoustics2012; 37: 455–462.
44.
Romero-GarcíaVSánchez-PérezJVGarcia-RaffiLM.Tunable wideband bandstop acoustic filter based on two-dimensional multiphysical phenomena periodic systems. J Appl Phys2011; 110: 014904.
45.
Romero-GarcíaVKrynkinAGarcia-RaffiL, et al. Multi-resonant scatterers in sonic crystals: Locally multi-resonant acoustic metamaterial. J Sound Vibrat2013; 332: 184–198.
46.
DhattG.TouzotG.Une présentation de la méthode des éléments finis. Presses Université Laval, 1981.
