The influences of the constituent material parameters of the three-dimensional locally resonant phononic crystal on the lower and upper edge frequencies of its lowest gap are investigated with the Multiple-scattering theory. It is found that the frequency dependence on those parameters can be well reproduced by a simple mass-spring model, which manifests the physical essence of the resonance modes determining the edge frequencies of the gap. Since the equivalent mass and stiffness of the model can be determined from the material parameters and structure size in one unit cell, the lower and upper edge frequencies of the lowest gap of locally resonant phononic crystals can be estimated from this model analytically. Comparison between the analytical estimations and the numerical results calculating with multiple scattering method shows very good agreement. The proposed heuristic model lends itself to understand the locally resonant mechanism more clearly. The frequency estimating formulas induced from the model allow one to predict the edge frequencies of the lowest gap, which simplifies the design process of locally resonant phononic crystals.

1.
Kushwaha
M. S.
;
Halevi
P.
;
Dobrzynski
L.
;
Djafari-Rouhani
B.
,
1993
, “
Acoustic Band Structure of Periodic Elastic Composites
,”
Phys. Rev. Lett.
,
71
,
2022
2025
.
2.
Martinez-Sala
R.
;
Sancho
J.
;
Sanchez
J. V.
;
Gomez
V.
;
Llinares
J.
;
Meseguer
F.
,
1995
, “
Sound attenuation by sculpture
,”
Nature
,
378
,
241
241
.
3.
Psarobas
I. E.
;
Stefanou
N.
;
Modinos
A.
,
2000
, “
Scattering of elastic waves by periodic arrays of spherical bodies
,”
Phys. Rev. B
,
62
,
278
291
.
4.
Cervera
F.
;
Sanchis
L.
;
Sanchez-Perez
J. V.
;
Martinez-Sala
R.
;
Rubio
C.
;
Meseguer
F.
;
Lopez
C.
;
Caballero
D.
;
Sanchez-Dehesa
J.
,
2002
, “
Refractive Acoustic Devices for Airborne Sound
,”
Phys. Rev. Lett.
,
88
,
023902
023902
.
5.
Khelif
A.
;
Choujaa
A.
;
Benchabane
S.
;
Djafari-Rouhani
B.
;
Laude
V.
,
2004
, “
Guiding and bending of acoustic waves in highly confined phononic crystal waveguides
,”
Appl. Phys. Lett.
,
84
,
4400
4402
.
6.
Liu
Z. Y.
,
Zhang
X. X.
;
Mao
Y. W.
,
Zhu
Y. Y.
,
Yang
Z. Y.
,
Chan
C. T.
,
Sheng
P.
,
2000
, “
Locally Resonant Sonic Materials
,”
Science
,
289
,
1734
1736
.
7.
Liu
Z. Y.
;
Chan
C. T.
;
Sheng
P.
,
2002
, “
Three-component elastic wave band-gap material
,”
Phys. Rev. B
,
65
,
165116
165116
.
8.
Goffaux
C
,
Sanchez-Dehesa
J
,
Yeyati
AL
, et al.,
2002
, “
Evidence of Fano-like interference phenomena in locally resonant materials
,”
Phys. Rev. Lett.
,
88
(
22
),
225
502
.
9.
Goffaux
C.
, and
Sa’nchez-Dehesa
Jose’
, “
Two-dimensional phononic crystals studied using a variational method: Application to lattices of locally resonant materials
,”
Phys. Rev. B
67
,
144301
144301
,
2003
10.
Zhang
X.
;
Liu
Y. Y.
;
Wu
F. G.
;
Liu
Z. Y.
,
2003
, “
Large two dimensional band gaps in three component phononic crystals
,”
Physics Letters A
,
317
,
144
149
.
11.
Ho
Kin Ming
,
Cheng
Chun Kwong
,
Yang
Z.
,
Zhang
X. X.
,
Sheng
Ping
,
2003
, “
Broadband locally resonant sonic shields
,”
Appl. Phys. Lett.
,
83
(
26
),
5566
5568
.
12.
Hirsekorn
M.
;
Delsanto
P. P.
;
Batra
N. K.
;
Matic
P.
,
2004
, “
Modeling and simulation of acoustic wave propagation in locally resonant sonic materials
,”
Ultrasonics
,
42
,
231
235
.
13.
Hirsekorn
M.
2004
, “
Small-size sonic crystals with strong attenuation bands in the audible frequency range
,”
Appl. Phys. Lett.
,
84
,
3364
3366
.
14.
Wang
Gang
,
Wen
Xisen
,
Wen
Jihong
,
Shao
Lihui
,
Liu
Yaozong
,
2004
, “
Two-Dimensional Locally Resonant Phononic Crystals with Binary Structures
,”
Phys. Rev. Lett.
,
93
(
15
),
154302
154302
.
15.
Liu
Z. Y.
;
Chan
C. T.
;
Sheng
P.
;
Goertzen
A. L.
;
Page
J. H.
,
2000
, “
Elastic wave scattering by periodic structures of spherical objects: Theory and experiment
,”
Phys. Rev. B
,
62
(
4
),
2446
2457
.
This content is only available via PDF.
You do not currently have access to this content.