This paper presents the wave propagation in a tunable phononic crystal consisting of a porous hyperelastic magnetorheological elastomer (MRE) subjected to an external magnetic field. Finite deformations and magnetic induction influence phononic characteristics of the periodic structure through altering the geometry and material properties of the unit cell. The governing equations for incremental time-harmonic plane wave motions superimposed on a static predeformed media are derived. Analytical and finite element (FE) methods are used to investigate dispersion relation and band structure of the phononic crystal for different levels of deformation and applied magnetic induction. It is demonstrated that large deformations and magnetic induction could transform the location and width of band-gaps.

References

References
1.
Yeh
,
J.
,
2007
, “
Control Analysis of the Tunable Phononic Crystal With Electrorheological Material
,”
Physica B
,
400
(
1–2
), pp.
137
144
.10.1016/j.physb.2007.06.030
2.
Shmuel
,
G.
,
2013
, “
Electrostatically Tunable Band Gaps in Finitely Extensible Dielectric Elastomer Fiber Composites
,”
Int. J. Solids Struct.
,
50
(
5
), pp.
680
686
.10.1016/j.ijsolstr.2012.10.028
3.
Wang
,
Y. Z.
,
Li
,
F. M.
,
Kishimoto
,
K.
,
Wang
,
Y. S.
, and
Huang
,
W. H.
,
2010
, “
Band Gaps of Elastic Waves in Three-Dimensional Piezoelectric Phononic Crystals With Initial Stress
,”
Eur. J. Mech. A.
, Solids,
29
(
2
), pp.
182
189
.10.1016/j.euromechsol.2009.09.005
4.
Wang
,
Y.
,
Li
,
F.
,
Kishimoto
,
K.
,
Wang
,
Y.
,
Huang
,
W.
, and
Jiang
,
X.
,
2009
, “
Elastic Wave Band Gaps in Magnetoelectroelastic Phononic Crystals
,”
Wave Motion
,
46
(
1
), pp.
47
56
.10.1016/j.wavemoti.2008.08.001
5.
Robillard
,
J.
,
BouMatar
,
O.
,
Vasseur
,
J. O.
,
Deymier
,
P. A.
,
Stippinger
,
M.
,
Hladky-Hennion
,
A.
,
Pennec
,
Y.
, and
Djafari-Rouhani
,
B.
,
2009
, “
Tunable Magnetoelastic Phononic Crystals
,”
Appl. Phys. Lett.
,
95
(
12
), p.
124104
.10.1063/1.3236537
6.
Bayat
,
A.
, and
Gordaninejad
,
F.
,
2014
, “
A Magnetically Field-Controllable Phononic Crystal
,”
Proc. SPIE
,
9057
, p.
905713
.10.1117/12.2046345
7.
Xu
,
Z.
,
Wu
,
F.
, and
Guo
,
Z.
,
2013
, “
Shear-Wave Band Gaps Tuned in Two-Dimensional Phononic Crystals With Magnetorheological Material
,”
Solid State Commun.
,
154
, pp.
43
45
.10.1016/j.ssc.2012.10.040
8.
Bou Matar
,
O.
,
Robillard
,
J. F.
,
Vasseur
,
J. O.
,
Hladky-Hennion
,
A.-C.
,
Deymier
,
P. A.
,
Pernod
,
P.
, and
Preobrazhensky
,
V.
,
2012
, “
Band Gap Tunability of Magneto-Elastic Phononic Crystal
,”
J. Appl. Phys.
,
111
(
5
), p.
054901
.10.1063/1.3687928
9.
Ding
,
R.
,
Su
,
X.
,
Zhang
,
J.
, and
Gao
,
Y.
,
2014
, “
Tunability of Longitudinal Wave Band Gaps in One Dimensional Phononic Crystal with Magnetostrictive Material
,”
J. Appl. Phys.
,
115
(
7
), p.
074104
.10.1063/1.4866364
10.
Deymier
,
P. A.
,
2013
,
Acoustic Metamaterials and Phononic Crystals
,
Springer, Berlin, Germany
, p.
253
.
11.
Dorfmann
,
A.
,
Ogden
,
R. W.
, and
Saccomandi
,
G.
,
2006
, “
Universal Relations for Nonlinear Magnetoelastic Solids
,”
Int. J. Non-Linear Mech.
,
39
(
10
), pp.
1699
1708
.10.1016/j.ijnonlinmec.2004.03.002
12.
Bustamante
,
R.
,
Dorfmann
,
A.
, and
Ogden
,
R. W.
,
2011
, “
Numerical Solution of Finite Geometry Boundary-Value Problems in Nonlinear Magnetoelasticity
,”
Int. J. Solids Struct.
,
48
(
6
), pp.
874
883
.10.1016/j.ijsolstr.2010.11.021
13.
Dorfmann
,
A. L.
, and
Ogden
,
R. W.
,
2014
,
Nonlinear Theory of Electroelastic and Magnetoelastic Interactions
,
Springer
,
Berlin, Germany
, p.
91
.
14.
Saxena
,
P.
,
2012
, “
On Wave Propagation in Finitely Deformed Magnetoelastic Solids
,” Ph.D. thesis, University of Glasgow, Glasgow, UK.
15.
Ogden
,
R. W.
,
2009
, “
Incremental Elastic Motions Superimposed on a Finite Deformation in the Presence Of an Electromagnetic Field
,”
Int. J. Non-Linear Mech.
,
44
(
5
), pp.
570
580
.10.1016/j.ijnonlinmec.2008.11.017
16.
Otténio
,
M.
,
Destrade
,
M.
, and
Ogden
,
R. W.
,
2008
, “
Incremental Magnetoelastic Deformations With Application to Surface Instability
,”
J. Elasticity
,
90
(
1
), pp.
19
42
.10.1007/s10659-007-9120-6
17.
Destrade
,
M.
, and
Ogden
,
R. W.
,
2011
, “
On Magneto-Acoustic Waves in Finitely Deformed Elastic Solids
,”
Math. Mech. Solids
,
16
(
6
), pp.
594
604
.10.1177/1081286510387695
18.
Bertoldi
,
K.
,
Boyce
,
M. C.
,
Deschanel
,
S.
,
Prange
,
S. M.
, and
Mullin
,
T.
,
2008
, “
Mechanics of Deformation-Triggered Pattern Transformations and Superelastic Behavior in Periodic Elastomeric Structures
,”
J. Mech. Phys. Solids
,
56
(
8
), pp.
2642
2668
.10.1016/j.jmps.2008.03.006
19.
Bertoldi
,
K.
, and
Boyce
,
M. C.
,
2008
, “
Wave Propagation and Instabilities in Monolithic and Periodically Structured Elastomeric Materials Undergoing Large Deformations
,”
Phys. Rev. B
,
78
(
18
), p.
184107
.10.1103/PhysRevB.78.184107
20.
Triantafyllidis
,
N.
,
Nestorovic
,
M. D.
, and
Schraad
,
M. W.
,
2006
, “
Failure Surfaces for Finitely Strained Two-Phase Periodic Solids Under General In-Plane Loading
,”
ASME J. Appl. Mech.
,
73
(
3
), pp.
505
515
.10.1115/1.2126695
21.
Holzapfel
,
G. A.
,
2000
,
Nonlinear Solid Mechanics: A Continuum Approach for Engineering
,
Wiley
,
Chichester, UK
.
You do not currently have access to this content.