This paper reports a comprehensive modeling and experimental characterization of a three-dimensional phononic crystal composed of a single material, endowed with an ultra-wide complete bandgap. The phononic band structure shows a gap-mid gap ratio of 132% that is by far the greatest full 3D bandgap in literature for any kind of phononic crystals. A prototype of the finite crystal structure has been manufactured in polyamide by means of additive manufacturing technology and tested to assess the transmission spectrum of the crystal. The transmission spectrum has been numerically calculated taking into account a frequency-dependent elastic modulus and a Rayleigh model for damping. The measured and numerical transmission spectra are in good agreement and present up to 75 dB of attenuation for a three-layer crystal.

1.
L.
Brillouin
,
Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices
(
Dover Publications, Inc.
,
New York
,
1946
).
2.
C.
Kittel
,
Introduction to Solid State Physics
, 8th ed. (
Wiley
,
2004
).
3.
J.
Joannopoulos
,
S.
Johnson
,
J.
Winn
, and
R.
Meade
,
Photonic Crystals: Molding the Flow of Light
, 2nd ed. (
Princeton University Press
,
2011
).
4.
P.
Deymier
,
Acoustic Metamaterials and Phononic Crystals
(
Springer-Verlag
,
Berlin, Heidelberg
,
2013
).
5.
M.
Hussein
,
M.
Leamy
, and
M.
Ruzzene
, “
Dynamics of phononic materials and structures: Historical origins, recent progress, and future outlook
,”
Appl. Mech. Rev.
66
,
040802
(
2014
).
6.
V.
Laude
,
Phononic Crystals: Artificial Crystals for Sonic, Acoustic, and Elastic Waves
(
De Gruyter
,
2015
).
7.
M.
Maldovan
, “
Sound and heat revolutions in phononics
,”
Nature
503
,
209
217
(
2013
).
8.
V.
Laude
, “
General solution of the coupled-wave equations of acousto-optics
,”
J. Opt. Soc. Am. A
20
,
2307
2314
(
2003
).
9.
A.
Khelif
,
B.
Djafari-Rouhani
,
V.
Laude
, and
M.
Solal
, “
Coupling characteristics of localized phonons in photonic crystal fibers
,”
J. Appl. Phys.
94
,
7944
7946
(
2003
).
10.
M.
Maldovan
and
E.
Thomas
, “
Simultaneous localization of phonons and photons in two-dimensional periodic structures
,”
Appl. Phys. Lett.
88
,
251907
(
2006
).
11.
S.
El-Jallal
,
M.
Oudich
,
Y.
Pennec
,
B.
Djafari-Rouhani
,
V.
Laude
,
J.-C.
Beugnot
,
A.
Martínez
,
J.
Escalante
, and
A.
Makhoute
, “
Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities
,”
Phys. Rev. B
88
,
205410
(
2013
).
12.
O.
Sigmund
and
J.
Jensen
, “
Systematic design of phononic band-gap materials and structures by topology optimization
,”
Philos. Trans. R. Soc., A
361
,
1001
1019
(
2003
).
13.
G.
Gazonas
,
D.
Weile
,
R.
Wildman
, and
A.
Mohan
, “
Genetic algorithm optimization of phononic bandgap structures
,”
Int. J. Solids Struct.
43
,
5851
5866
(
2006
).
14.
O.
Bilal
and
M.
Hussein
, “
Ultrawide phononic band gap for combined in-plane and out-of-plane waves
,”
Phys. Rev. E
84
,
065701(R)
(
2011
).
15.
J.-H.
Lee
,
C.
Koh
,
J.
Singer
,
S.-J.
Jeon
,
M.
Maldovan
,
O.
Stein
, and
E.
Thomas
, “
25th anniversary article: Ordered polymer structures for the engineering of photons and phonons
,”
Adv. Mater.
26
,
532
569
(
2014
).
16.
X.
Zhang
,
Z.
Liu
,
Y.
Liu
, and
F.
Wu
, “
Elastic wave band gaps for three-dimensional phononic crystals with two structural units
,”
Phys. Lett. A
313
,
455
460
(
2003
).
17.
T.
Delpero
,
S.
Schoenwald
,
A.
Zemp
, and
A.
Bergamini
, “
Structural engineering of three-dimensional phononic crystals
,”
J. Sound Vib.
363
,
156
165
(
2016
).
18.
F.
Lucklum
and
M.
Vellekoop
, “
Realization of complex 3-D phononic crystals with wide complete acoustic band gaps
,”
IEEE Trans. Ultrason. Ferroelectr.
63
,
796
797
(
2016
).
19.
S.
Babaee
,
P.
Wang
, and
K.
Bertoldi
, “
Three-dimensional adaptive soft phononic crystals
,”
J. Appl. Phys.
117
,
244903
(
2015
).
20.
T.-X.
Ma
,
Y.-S.
Wang
,
Y.-F.
Wang
, and
X.-X.
Su
, “
Three-dimensional dielectric phoxonic crystals with network topology
,”
Opt. Express
21
,
2727
2732
(
2013
).
21.
L.
D'Alessandro
,
B.
Bahr
,
L.
Daniel
,
D.
Weinstein
, and
R.
Ardito
, “
BESO approach to topology optimization of GaN phononic crystals
,” in
VII European Congress on Computational Methods in Applied Sciences and Engineering
(
2016
).
22.
It must be noted that the optimal topology strongly depends on the thickness of the slab and on the elastic parameters of the material adopted.
23.
S.
Hedayatrasa
,
K.
Abhary
,
M.
Uddin
, and
C.-T.
Ng
, “
Optimum design of phononic crystal perforated plate structures for widest bandgap of fundamental guided wave modes and maximized in-plane stiffness
,”
J. Mech. Phys. Solids
89
,
31
58
(
2016
).
24.
EOS GmbH—Electro Optical Systems, “PA 2200—material data sheet.”
25.
B.
Merheb
,
P.
Deymier
,
M.
Jain
,
M.
Aloshyna-Lesuffleur
,
S.
Mohanty
,
A.
Berker
, and
R.
Greger
, “
Elastic and viscoelastic effects in rubber/air acoustic band gap structures: A theoretical and experimental study
,”
J. Appl. Phys.
104
,
064913
(
2008
).
26.
B.
Cotté
,
A.
Parret-Fréaud
, and
A.
Chaigne
, “
Measurement and modeling of damping for time-domain structural acoustics simulations
,” in
Noise-Con 2013
(
Denver, CO, USA
,
2013
).
27.
P.
Collet
,
G.
Gary
, and
B.
Lundberg
, “
Noise-corrected estimation of complex modulus in accord with causality and thermodynamics: Application to an impact test
,”
J. Appl. Mech.
80
,
011018
(
2013
).
28.
M.
Hussein
and
M.
Frazier
, “
Band structure of phononic crystals with general damping
,”
J. Appl. Phys.
108
,
093506
(
2010
).
29.
K.
Matlack
,
A.
Bauhofer
,
S.
Krödel
,
A.
Palermo
, and
C.
Daraio
, “
Composite 3D-printed metastructures for low-frequency and broadband vibration absorption
,”
Proc. Natl. Acad. Sci.
113
,
8386
8390
(
2016
).
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