Broad omnidirectional band gaps in a three-dimensional phononic crystal consisting of a face-centered cubic array of spherical air voids connected by cylindrical conduits in solid background are numerically and experimentally demonstrated. With a low material filling fraction of 37.7%, the first bandgap covers 3.1–13.6 kHz frequency range with 126.1% gap-over-midgap ratio. Finite-element method is employed in band structure and numerical transmission analyses. Omnidirectional band gaps are observed in only two-period thick slabs in the , , and orientations. Experimental transmission characteristics are in good agreement with numerical data. The phononic crystal can be employed in low-frequency sound proofing.
References
1.
M. S.
Kushwaha
, P.
Halevi
, L.
Dobrzynski
, and B.
Djafari-Rouhani
, “Acoustic band structure of periodic elastic composites
,” Phys. Rev. Lett.
71
, 2022
–2025
(1993
).2.
M.
Kushwaha
and B.
Djafari-Rouhani
, “Complete acoustic stop bands for cubic arrays of spherical liquid balloons
,” J. Appl. Phys.
80
, 3191
–3195
(1996
).3.
B.
Assouar
, R.
Sainidou
, and I.
Psarobas
, Phononic Crystals: Fundamentals and Applications
(Springer
, New York
, 2016
), pp. 51
–83
.4.
H.
Jiang
and Y.
Chen
, “Lightweight architected hollow sphere foams for simultaneous noise and vibration control
,” J. Phys. D: Appl. Phys.
52
, 325303
(2019
).5.
Z.
Liu
, X.
Zhang
, Y.
Mao
, Y.
Zhu
, Z.
Yang
, C. T.
Chan
, and P.
Sheng
, “Locally resonant sonic materials
,” Science
289
, 1734
–1736
(2000
).6.
A.
Khelif
, F.-L.
Hsiao
, A.
Choujaa
, S.
Benchabane
, and V.
Laude
, “Octave omnidirectional band gap in a three-dimensional phononic crystal
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
57
, 1621
–1625
(2010
).7.
N.
Aravantinos-Zafiris
and M.
Sigalas
, “Band gaps in three-dimensional layer-by-layer phononic crystal
,” J. Vib. Acoust.
135
, 041003
(2013
).8.
L.-Y.
Wu
and L.-W.
Chen
, “Acoustic band gaps of the woodpile sonic crystal with the simple cubic lattice
,” J. Phys. D: Appl. Phys.
44
, 045402
(2011
).9.
Y.
Chen
, H.
Yao
, and L.
Wang
, “Acoustic band gaps of three-dimensional periodic polymer cellular solids with cubic symmetry
,” J. Appl. Phys.
114
, 043521
(2013
).10.
C.
Croënne
, E.
Lee
, H.
Hu
, and J.
Page
, “Band gaps in phononic crystals: Generation mechanisms and interaction effects
,” AIP Adv.
1
, 041401
(2011
).11.
F.
Lucklum
and M.
Vellekoop
, “Bandgap engineering of three-dimensional phononic crystals in a simple cubic lattice
,” Appl. Phys. Lett.
113
, 201902
(2018
).12.
O. R.
Bilal
, D.
Ballagi
, and C.
Daraio
, “Architected lattices for simultaneous broadband attenuation of airborne sound and mechanical vibrations in all directions
,” Phys. Rev. Appl.
10
, 054060
(2018
).13.
X.
Hu
, C. T.
Chan
, and J.
Zi
, “Two-dimensional sonic crystals with Helmholtz resonators
,” Phys. Rev. E
71
, 055601
(2005
).14.
L.
Chalmers
, D.
Elford
, F.
Kusmartsev
, and G.
Swallowe
, “Acoustic band gap formation in two-dimensional locally resonant sonic crystals comprised of Helmholtz resonators
,” Int. J. Mod. Phys. B
23
, 4234
–4243
(2009
).15.
Z. G.
Wang
, S. H.
Lee
, C. K.
Kim
, C. M.
Park
, K.
Nahm
, and S.
Nikitov
, “Acoustic wave propagation in one-dimensional phononic crystals containing Helmholtz resonators
,” J. Appl. Phys.
103
, 064907
(2008
).16.
Y.
Cheng
, J.
Xu
, and X.
Liu
, “Broad forbidden bands in parallel-coupled locally resonant ultrasonic metamaterials
,” Appl. Phys. Lett.
92
, 051913
(2008
).17.
J.-B.
Li
, Y.-S.
Wang
, and C.
Zhang
, “Complete bandgap in three-dimensional holey phononic crystals with resonators
,” J. Vib. Acoust.
135
, 031015
(2013
).18.
F.
Lucklum
and M.
Vellekoop
, “Design and fabrication challenges for millimeter-scale three-dimensional phononic crystals
,” Crystals
7
, 348
(2017
).19.
F.
Lucklum
and M.
Vellekoop
, “Rapid prototyping of 3D phononic crystals using high-resolution stereolithography fabrication
,” Procedia Eng.
120
, 1095
–1098
(2015
).20.
F.
Lucklum
and M. J.
Vellekoop
, “Realization of complex 3-D phononic crystals with wide complete acoustic band gaps
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control.
63
, 796
–797
(2016
).21.
N.
Korozlu
, O. A.
Kaya
, A.
Cicek
, and B.
Ulug
, “Acoustic Tamm states of three-dimensional solid-fluid phononic crystals
,” J. Acoust. Soc. Am.
143
, 756
–764
(2018
).22.
N.
Aravantinos-Zafiris
, F.
Lucklum
, and M. M.
Sigalas
, “Complete phononic band gaps in the 3D Yablonovite structure with spheres
,” Ultrasonics
110
, 106265
(2021
).23.
F.
Cervera
, L.
Sanchis
, J. V.
Sánchez-Pérez
, R.
Martínez-Sala
, C.
Rubio
, F.
Meseguer
, C.
López
, D.
Caballero
, and J.
Sánchez-Dehesa
, “Refractive Acoustic Devices for Airborne Sound
,” Phys. Rev. Lett.
88
, 023902
(2001
).24.
Y.
Jin
, B.
Djafari-Rouhani
, and D.
Torrent
, “Gradient index phononic crystals and metamaterials
,” Nanophotonics.
8
, 685
–701
(2019
).25.
D. R.
Raichel
, The Science and Applications of Acoustics
(Springer Science & Business Media
, New York
, 2006
), pp. 145
–148
.26.
M.
Molerón
, M.
Serra-Garcia
, and C.
Daraio
, “Visco-thermal effects in acoustic metamaterials: From total transmission to total reflection and high absorption
,” New J. Phys.
18
, 033003
(2016
).27.
X.
Jiang
, Y.
Li
, and L.
Zhang
, “Thermoviscous effects on sound transmission through a metasurface of hybrid resonances
,” J. Acoust. Soc. Am.
141
, EL363
–EL638
(2017
).28.
J.-P.
Berenger
, “Perfectly matched layer for the FDTD solution of wave-structure interaction problems
,” IEEE Trans. Antennas Propag.
44
, 110
–117
(1996
).29.
V.
Fokin
, M.
Ambati
, C.
Sun
, and X.
Zhang
, “Method for retrieving effective properties of locally resonant acoustic metamaterials
,” Phys. Rev. B
76
, 144302
(2007
).© 2021 Acoustical Society of America.
2021
Acoustical Society of America
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