In this paper, the problem of in-plane wave propagation with oblique incidence of the wave in an isotropic bilaminated composite under perfect contact between the layers and periodic distribution between them is studied. Based on an asymptotic dispersive method for the description of the dynamic processes, the dispersion equations were derived analytically from the average model. Numerical examples show that the dispersion curves obtained from the present model agree with the exact solutions for a range of wavelengths. Detailed numerical simulations are provided to illustrate graphically the phase and group velocities. Such illustrations allow the identification and comparison of the effects of the unit cell size, wave number and incident angle. It was observed that, as the incident angle increases, the dimensionless quasi-longitudinal phase velocity increases, and the dimensionless quasi-shear phase velocity decreases. In addition, the phase and group velocities decrease as the size of the unit cell increases. The frequency band structure, as a function of the wave-vector components is calculated.

References

References
1.
Hill
,
R.
,
1965
, “
A Self-Consistent Mechanics of Composite Materials
,”
J. Mech. Phys. Solids
,
13
(
4
), pp.
213
222
.10.1016/0022-5096(65)90010-4
2.
Beran
,
M.
,
1968
,
Statistical Continuum Theories
,
Wiley
,
New York
.
3.
Willis
,
J. R.
,
2009
, “
Exact Effective Relations for Dynamics of a Laminated Body
,”
Mech. Mater.
,
41
(
4
), pp.
385
393
.10.1016/j.mechmat.2009.01.010
4.
Willis
,
J. R.
,
2011
, “
Effective Constitutive Relations for Waves in Composites and Metamaterials
,”
Proc. R. Soc. London, Ser. A
,
467
(2131), pp.
1865
1879
.10.1098/rspa.2010.0620
5.
Willis
,
J. R.
,
2012
, “
The Construction of Effective Relations for Waves in a Composite
,”
C. R. Mec.
,
340
(
4–5
), pp.
181
192
.10.1016/j.crme.2012.02.001
6.
Mazur-Sniady
,
K.
,
Wozniak
,
C.
, and
Wierzbicki
,
E.
,
2004
, “
On the Modelling of the Dynamic Problems for Plates With a Periodic Structure
,”
Arch. Appl. Mech.
,
74
(
3–4
), pp.
179
190
.10.1007/s00419-003-0310-9
7.
Smyshlyaev
,
V.
,
2009
, “
Propagation and Localization of Elastic Waves in Highly Anisotropic Periodic Composites Via Two-Scale Homogenization
,”
Mech. Mater.
,
41
(
4
), pp.
434
447
.10.1016/j.mechmat.2009.01.009
8.
Chen
,
W.
, and
Fish
,
J.
,
2001
, “
A Dispersive Model for Wave Propagation in Periodic Heterogeneous Media Based on Homogenization With Multiple Spatial and Temporal Scales
,”
ASME J. Appl. Mech.
,
68
(
2
), pp.
153
161
.10.1115/1.1357165
9.
Nemat-Nasser
,
S.
, and
Srivastava
,
A.
,
2011
, “
Overall Dynamic Constitutive Relations of Layered Elastic Composites
,”
J. Mech. Phys. Solids
,
59
(
10
), pp.
1953
1965
.10.1016/j.jmps.2011.07.008
10.
Nemat-Nasser
,
S.
,
Willis
,
J. R.
,
Srivastava
,
A.
, and
Amirkhizi
,
A. V.
,
2011
, “
Homogenization of Periodic Elastic Composites and Locally Resonant Sonic Materials
,”
Phys. Rev. B
,
83
(
10
), p.
104103
.10.1103/PhysRevB.83.104103
11.
Kim
,
J.
,
2004
, “
On the Generalized Self-Consistent Model for Elastic Wave Propagation in Composite Materials
,”
Int. J. Solids Struct.
,
41
(
16–17
), pp.
4349
4360
.10.1016/j.ijsolstr.2004.03.020
12.
António
,
J.
,
Tadeu
,
A.
, and
Godinho
,
L.
,
2005
, “
2.5D Scattering of Waves by Rigid Inclusions Buried Under a Fluid Channel Via BEM
,”
Eur. J. Mech. A: Solids
,
24
(
6
), pp.
957
973
.10.1016/j.euromechsol.2005.04.002
13.
Fang
,
X. Q.
,
Wang
,
D. B.
, and
Liu
,
J. X.
,
2009
, “
Multiple Scattering of Elastic Waves in Metal-Matrix Composite Materials With High Volume Concentration of Particles
,”
Eur. J. Mech. A: Solids
,
28
(
2
), pp.
377
386
.10.1016/j.euromechsol.2008.09.004
14.
Wang
,
J. H.
,
Lu
,
J. F.
, and
Zhou
,
X. L.
,
2009
, “
Complex Variable Function Method for the Scattering of Plane Waves by an Arbitrary Hole in a Porous Medium
,”
Eur. J. Mech. A: Solids
,
28
(
3
), pp.
582
590
.10.1016/j.euromechsol.2008.09.005
15.
Molero
,
M.
,
Segura
,
I.
,
Hernández
,
M. G.
,
Izquierdo
,
M. A. G.
, and
Anaya
,
J. J.
,
2011
, “
Ultrasonic Wave Propagation in Cementitious Materials: A Multiphase Approach of a Self-Consistent Multiple Scattering Model
,”
Ultrasonics
,
51
(
1
), pp.
71
84
.10.1016/j.ultras.2010.06.001
16.
Parnell
,
W. J.
, and
Abrahams
,
I. D.
,
2006
, “
Dynamic Homogenization in Periodic Fibre Reinforced Media: Quasi-Static Limit for SH Waves
,”
Wave Motion
,
43
(
6
), pp.
474
498
.10.1016/j.wavemoti.2006.03.003
17.
Parnell
,
W. J.
, and
Abrahams
,
I. D.
,
2008
, “
Homogenization for Wave Propagation in Periodic Fiber-Reinforced Media With Complex Microstructure. I—Theory
,”
J. Mech. Phys. Solids
,
56
(
7
), pp.
2521
2540
.10.1016/j.jmps.2008.02.003
18.
Vivar-Pérez
,
J. M.
,
Gabbert
,
U.
,
Berger
,
H.
,
Rodríguez-Ramos
,
R.
,
Bravo-Castillero
,
J.
,
Guinovat-Díaz
,
R.
, and
Sabina
,
F. J.
,
2009
, “
A Dispersive Nonlocal Model for Wave in Periodic Composites
,”
J. Mech. Mater. Struct.
,
4
(
5
), pp.
951
976
.10.2140/jomms.2009.4.951
19.
Brito-Santana
,
H.
,
Wang
,
Y. S.
,
Rodríguez-Ramos
,
R.
,
Bravo-Castillero
,
J.
,
Guinovart-Díaz
,
R.
, and
Volnei
,
T.
,
2015
, “
A Dispersive Nonlocal Model for Shear Wave Propagation in Laminated Composites With Periodic Structures
,”
Eur. J. Mech. A: Solids
,
49
, pp.
35
48
.10.1016/j.euromechsol.2014.05.009
20.
Sun
,
C. T.
,
Achenbach
,
J. D.
, and
Herrmann
,
G.
,
1968
, “
Continuum Theory for a Laminated Medium
,”
ASME J. Appl. Mech.
,
35
(
3
), pp.
467
475
.10.1115/1.3601237
21.
Oleinik
,
O. A.
,
Shamaev
,
A. S.
, and
Yosifian
,
G. A.
,
1992
,
Mathematical Problems in Elasticity and Homogenization
,
North-Holland
,
Amsterdam
.
22.
Sanchez-Palencia
,
E.
,
1980
,
Non-Homogeneous Media and Vibration Theory
(Lecture Notes in Physics, Vol.
127
),
Springer-Verlag
,
Berlin
.
23.
Bakhalov
,
N.
, and
Panasenko
,
G.
,
1989
,
Homogenization: Averaging Processes in Periodic Media
,
Kluwer
,
Dordrecht
.
24.
Bensoussan
,
A.
,
Papanicolaou
,
G.
, and
Lions
,
J. L.
,
1978
,
Asymptotic Analysis for Periodic Structure
,
North Holland
,
Amsterdam
.
25.
Amirkhizi
,
A. V.
,
Tehranian
,
A.
, and
Nemat-Nasser
,
S.
,
2010
, “
Stress-Wave Energy Management Through Material Anisotropy
,”
Wave Motion
,
47
(
8
), pp.
519
536
.10.1016/j.wavemoti.2010.03.005
26.
Graff
,
K. F.
,
1991
,
Wave Motion in Elastic Solids
,
Dover
,
New York
.
27.
Wang
,
Z. P.
, and
Sun
,
C. T.
,
2002
, “
Modeling Micro-Inertia in Heterogeneous Materials Under Dynamic Loading
,”
Wave Motion
,
36
(
4
), pp.
473
485
.10.1016/S0165-2125(02)00037-9
28.
Verbis
,
J. T.
,
Kattis
,
S. E.
,
Tsinopoulos
,
S. V.
, and
Polyzos
,
D.
,
2001
, “
Wave Dispersion and Attenuation in Fiber Composites
,”
Comput. Mech.
,
27
(
3
), pp.
244
252
.10.1007/s004660000226
29.
Achenbach
,
J. D.
,
1973
,
Wave Propagation in Elastic Solids
,
North Holland
,
Amsterdam
.
30.
Kalamkarov
,
A. L.
,
1992
,
Composite and Reinforced Elements of Construction
,
Wiley
,
Chichester, UK
.
You do not currently have access to this content.