Solid structures guide a multitude of elastic modes of different polarizations including both compression and shear, and the nature of the elastic constant tensor implies a much richer behavior than in optics. Here, we introduce a metamaterial in the form of a rectangular cross section beam of a single isotropic material that can simultaneously suppress all elastic-wave polarizations in the beam over a range of frequencies in the kHz range. This is experimentally achieved by machining replicas of a subwavelength unit cell in an aluminum metabeam based on a planar resonator with interconnected ribs, showing complex vibrational degrees of freedom that allow it to couple to compressional, in-plane shear, flexural and torsional vibrations, that is, all four existing mode types. The result is a lightweight structure that can forbid all possible acoustic modes over the metamaterial bandgap frequency range, an exotic behavior that opens up diverse applications in easily manufacturable vibration isolation structures and acoustic wave control.

1.
J. B.
Pendry
,
A. J.
Holden
,
D. J.
Robbins
,
W.
Stewart
 et al, “
Magnetism from conductors and enhanced nonlinear phenomena
,”
IEEE Trans. Microwave Theory Tech.
47
,
2075
2084
(
1999
).
2.
D. R.
Smith
,
W. J.
Padilla
,
D.
Vier
,
S. C.
Nemat-Nasser
, and
S.
Schultz
, “
Composite medium with simultaneously negative permeability and permittivity
,”
Phys. Rev. Lett.
84
,
4184
(
2000
).
3.
R. A.
Shelby
,
D. R.
Smith
, and
S.
Schultz
, “
Experimental verification of a negative index of refraction
,”
Science
292
,
77
79
(
2001
).
4.
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
).
5.
V. M.
García-Chocano
,
J.
Christensen
, and
J.
Sánchez-Dehesa
, “
Negative refraction and energy funneling by hyperbolic materials: An experimental demonstration in acoustics
,”
Phys. Rev. Lett.
112
,
144301
(
2014
).
6.
R.
Zhu
,
X.
Liu
,
G.
Hu
,
C.
Sun
, and
G.
Huang
, “
Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial
,”
Nat. Commun.
5
,
5510
(
2014
).
7.
S.
Zhang
,
L.
Yin
, and
N.
Fang
, “
Focusing ultrasound with an acoustic metamaterial network
,”
Phys. Rev. Lett.
102
,
194301
(
2009
).
8.
L.
Zigoneanu
,
B.-I.
Popa
, and
S. A.
Cummer
, “
Design and measurements of a broadband two-dimensional acoustic lens
,”
Phys. Rev. B
84
,
024305
(
2011
).
9.
F.
Lemoult
,
N.
Kaina
,
M.
Fink
, and
G.
Lerosey
, “
Soda cans metamaterial: a subwavelength-scaled phononic crystal
,”
Crystals
6
,
82
(
2016
).
10.
J.
Pendry
and
J.
Li
, “
An acoustic metafluid: realizing a broadband acoustic cloak
,”
New J. Phys.
10
,
115032
(
2008
).
11.
A. N.
Norris
, “
Acoustic metafluids
,”
J. Acoust. Soc. Am.
125
,
839
849
(
2009
).
12.
N.
Stenger
,
M.
Wilhelm
, and
M.
Wegener
, “
Experiments on elastic cloaking in thin plates
,”
Phys. Rev. Lett.
108
,
014301
(
2012
).
13.
T.
Bückmann
,
M.
Thiel
,
M.
Kadic
,
R.
Schittny
, and
M.
Wegener
, “
An elasto-mechanical unfeelability cloak made of pentamode metamaterials
,”
Nat. Commun.
5
,
4130
(
2014
).
14.
N.
Fang
,
D.
Xi
,
J.
Xu
,
M.
Ambati
,
W.
Srituravanich
,
C.
Sun
, and
X.
Zhang
, “
Ultrasonic metamaterials with negative modulus
,”
Nat. Mater.
5
,
452
(
2006
).
15.
S.
Yao
,
X.
Zhou
, and
G.
Hu
, “
Experimental study on negative effective mass in a 1d mass–spring system
,”
New J. Phys.
10
,
043020
(
2008
).
16.
P. H.
Otsuka
,
S.
Mezil
,
O.
Matsuda
,
M.
Tomoda
,
A. A.
Maznev
,
T.
Gan
,
N.
Fang
,
N.
Boechler
,
V. E.
Gusev
, and
O. B.
Wright
, “
Time-domain imaging of gigahertz surface waves on an acoustic metamaterial
,”
New J. Phys.
20
,
013026
(
2018
).
17.
D.
Yu
,
Y.
Liu
,
G.
Wang
,
H.
Zhao
, and
J.
Qiu
, “
Flexural vibration band gaps in timoshenko beams with locally resonant structures
,”
J. Appl. Phys.
100
,
124901
(
2006
).
18.
Y.
Xiao
,
J.
Wen
,
D.
Yu
, and
X.
Wen
, “
Flexural wave propagation in beams with periodically attached vibration absorbers: band-gap behavior and band formation mechanisms
,”
J. Sound Vib.
332
,
867
893
(
2013
).
19.
Y.
Xiao
,
J.
Wen
,
G.
Wang
, and
X.
Wen
, “
Theoretical and experimental study of locally resonant and bragg band gaps in flexural beams carrying periodic arrays of beam-like resonators
,”
J. Vib. Acoust.
135
,
041006
(
2013
).
20.
S.
Zhang
,
J.
Hui Wu
, and
Z.
Hu
, “
Low-frequency locally resonant band-gaps in phononic crystal plates with periodic spiral resonators
,”
J. Appl. Phys.
113
,
163511
(
2013
).
21.
R.
Zhu
,
X.
Liu
,
G.
Hu
,
C.
Sun
, and
G.
Huang
, “
A chiral elastic metamaterial beam for broadband vibration suppression
,”
J. Sound Vib.
333
,
2759
2773
(
2014
).
22.
M.
Nouh
,
O.
Aldraihem
, and
A.
Baz
, “
Vibration characteristics of metamaterial beams with periodic local resonances
,”
J. Vib. Acoust.
136
,
061012
(
2014
).
23.
H.
Zhang
,
Y.
Xiao
,
J.
Wen
,
D.
Yu
, and
X.
Wen
, “
Flexural wave band gaps in metamaterial beams with membrane-type resonators: theory and experiment
,”
J. Phys. D: Appl. Phys.
48
,
435305
(
2015
).
24.
G.
Ma
,
C.
Fu
,
G.
Wang
,
P.
Del Hougne
,
J.
Christensen
,
Y.
Lai
, and
P.
Sheng
, “
Polarization bandgaps and fluid-like elasticity in fully solid elastic metamaterials
,”
Nat Commun.
7
,
13536
(
2016
).
25.
T.
Wang
,
M.-P.
Sheng
, and
Q.-H.
Qin
, “
Multi-flexural band gaps in an Euler–Bernoulli beam with lateral local resonators
,”
Phys. Lett. A
380
,
525
529
(
2016
).
26.
L.
Li
and
A.
Cai
, “
Low-frequency band gap mechanism of torsional vibration of lightweight elastic metamaterial shafts
,”
Eur. Phys. J. Appl. Phys.
75
,
10501
(
2016
).
27.
E.
Nobrega
,
F.
Gautier
,
A.
Pelat
, and
J.
Dos Santos
, “
Vibration band gaps for elastic metamaterial rods using wave finite element method
,”
Mech. Syst. Signal Process.
79
,
192
202
(
2016
).
28.
L.
Tang
and
L.
Cheng
, “
Ultrawide band gaps in beams with double-leaf acoustic black hole indentations
,”
J. Acoust. Soc. Am.
142
,
2802
2807
(
2017
).
29.
H.
Chen
,
X.
Li
,
Y.
Chen
, and
G.
Huang
, “
Wave propagation and absorption of sandwich beams containing interior dissipative multi-resonators
,”
Ultrasonics
76
,
99
108
(
2017
).
30.
J.-S.
Chen
,
Y.-J.
Huang
, and
I.-T.
Chien
, “
Flexural wave propagation in metamaterial beams containing membrane-mass structures
,”
Int. J. Mech. Sci.
131–132
,
500
506
(
2017
).
31.
L.
Li
,
R.
Lv
,
A.
Cai
,
M.
Xie
,
Y.
Chen
, and
G.
Huang
, “
Low-frequency vibration suppression of a multi-layered elastic metamaterial shaft with discretized scatters
,”
J. Phys. D: Appl. Phys.
52
,
055105
(
2019
).
32.
K.
Wang
,
J.
Zhou
,
D.
Xu
, and
H.
Ouyang
, “
Tunable low-frequency torsional-wave band gaps in a meta-shaft
,”
J. Phys. D: Appl. Phys
52
,
055104
(
2019
).
33.
N. J.
Nigro
, “
Steady-state wave propagation in infinite bars of noncircular cross section
,”
J. Acoust. Soc. Am.
40
,
1501
1508
(
1966
).
34.
W.
Fraser
, “
Stress wave propagation in rectangular bars
,”
Int. J. Solids Struct.
5
,
379
397
(
1969
).
35.
R. D.
Mindlin
, “
Low frequency vibrations of elastic bars
,”
Int. J. Solids Struct.
12
,
27
49
(
1976
).
36.
F.-C.
Hsu
,
C.-I.
Lee
,
J.-C.
Hsu
,
T.-C.
Huang
,
C.-H.
Wang
, and
P.
Chang
, “
Acoustic band gaps in phononic crystal strip waveguides
,”
Appl. Phys. Lett.
96
,
051902
(
2010
).
37.
Y.
Pennec
,
B. D.
Rouhani
,
C.
Li
,
J.
Escalante
,
A.
Martínez
,
S.
Benchabane
,
V.
Laude
, and
N.
Papanikolaou
, “
Band gaps and cavity modes in dual phononic and photonic strip waveguides
,”
AIP Adv.
1
,
041901
(
2011
).
38.
F.-C.
Hsu
,
J.-C.
Hsu
,
T.-C.
Huang
,
C.-H.
Wang
, and
P.
Chang
, “
Reducing support loss in micromechanical ring resonators using phononic band-gap structures
,”
J. Phys. D: Appl. Phys.
44
,
375101
(
2011
).
39.
D.
Feng
,
D.
Xu
,
G.
Wu
,
B.
Xiong
, and
Y.
Wang
, “
Extending of band gaps in silicon based one-dimensional phononic crystal strips
,”
Appl. Phys. Lett.
103
,
151906
(
2013
).
40.
D.
Feng
,
D.
Xu
,
G.
Wu
,
B.
Xiong
, and
Y.
Wang
, “
Phononic crystal strip based anchors for reducing anchor loss of micromechanical resonators
,”
J. Appl. Phys.
115
,
024503
(
2014
).
41.
S.
Jiang
,
H.
Hu
, and
V.
Laude
, “
Low-frequency band gap in cross-like holey phononic crystal strip
,”
J. Phys. D: Appl. Phys.
51
,
045601
(
2018
).
42.
CRC Handbook of Chemistry and Physics
, 85th ed., edited by
D. R.
Lide
(
CRC Press
,
2004
).

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