Propagation of elastic waves in an infinite elastic medium containing a finite array of circular cylindrical cavities is considered. It is assumed that the cavities are equally spaced within each layer, but the cylinder radii, as well as the distance between the layers, may vary from layer to layer. Our objective is to analyze the effect of such an irregularity on scattering properties of the system. Using the method of multipole expansions we evaluate for the case of normal incidence the reflection and transmission matrices for a stack of layers, and find a range of frequencies for which polarization or complete reflection of an incident wave takes place. Presented results highlight the effect of variation in radii and distance between the layers on propagation of elastic waves in such structures.

Issue Section:
Technical Papers
Keywords:
elastic waves, wave propagation, arrays, inhomogeneous media
Topics:
Cavities, Diffraction gratings, Elastic waves, Electromagnetic scattering, Polarization (Electricity), Polarization (Light), Polarization (Waves), Waves, Reflection, Radiation scattering, Scattering (Physics), Cylinders
1.
Dowling, J. P., Everitt, H., and Yablonovitch, E., 2000, “Photonic and Sonic Band-Gap Bibliography,” http://home.earthlink.net/∼jpdowling/pbgbib.html
2.
Kushwaha
,
M. S.
,
Halevi
,
P.
,
Martinez
,
G.
,
Dobrzynski
,
L.
, and
Djafari-Rouhani
,
B.
,
1994
, “
Theory of Acoustic Band Structure of Periodic Elastic Composites
,”
Phys. Rev. B
,
49
, pp.
2313
–
2322
.
3.
Kushwaha
,
M. S.
, and
Halevi
,
P.
,
1994
, “
Band-Gap Engineering in Periodic Elastic Composites
,”
Appl. Phys. Lett.
,
64
, pp.
1085
–
1087
.
4.
Kushwaha
,
M. S.
, and
Halevi
,
P.
,
1996
, “
Giant Acoustic Stop Bands in Two-Dimensional Periodic Arrays of Liquid Cylinders
,”
Appl. Phys. Lett.
,
69
, pp.
31
–
33
.
5.
Kushwaha
,
M. S.
,
1997
, “
Stop-Bands for Periodic Metallic Rods: Sculptures That Can Filter the Noise
,”
Appl. Phys. Lett.
,
70
, pp.
3218
–
3220
.
6.
Poulton
,
C. G.
,
Movchan
,
A. B.
,
McPhedran
,
R. C.
,
Nicorovici
,
N. A.
, and
Antipov
,
Y. A.
,
2000
, “
Eigenvalue Problems for Doubly Periodic Elastic Structures and Phononic Band Gaps
,”
Proc. R. Soc. London, Ser. A
,
A456
, pp.
2543
–
2559
.
7.
Ball
,
P.
, 2002, “Sculpted Sound,” New Sci., March 23, 2002, pp. 32–35.
8.
Asatryan
,
A. A.
,
Robinson
,
P. A.
,
Botten
,
L. C.
,
McPhedran
,
R. C.
,
Nicorovici
,
N. A.
, and
de Sterke
,
C. M.
,
1999
, “
Effects of Disorder on Wave Propagation in Two-Dimensional Photonic Crystals
,”
Phys. Rev. E
,
60
, pp.
6118
–
6127
.
9.
Platts
,
S. B.
,
Movchan
,
N. V.
,
McPhedran
,
R. C.
, and
Movchan
,
A. B.
,
2002
,“
Two-Dimensional Phononic Crystals and Scattering of Elastic Waves by an Array of Voids
,”
Proc. R. Soc. London, Ser. A
,
A458
, pp.
2327
–
2347
.
10.
Twersky
,
V.
,
1961
, “
Elementary Function Representations of Schlo¨milch Series
,”
Arch. Ration. Mech. Anal.
,
8
, pp.
323
–
332
.
11.
Botten
,
L. C.
,
Nicorovici
,
N. A.
,
Asatryan
,
A. A.
,
McPhedran
,
R. C.
,
de Sterke
,
C. M.
, and
Robinson
,
P. A.
,
2000
, “
Formulation for Electromagnetic Scattering and Propagation Through Grating Stacks of Metallic and Dielectric Cylinders for Photonic Crystal Calculations. Part 1: Method
,”
J. Opt. Soc. Am.
,
A17
, pp.
2165
–
2176
.
12.
Botten
,
L. C.
,
Nicorovici
,
N. A.
,
Asatryan
,
A. A.
,
McPhedran
,
R. C.
,
de Sterke
,
C. M.
, and
Robinson
,
P. A.
,
2000
, “
Formulation for Electromagnetic Scattering and Propagation Through Grating Stacks of Metallic and Dielectric Cylinders for Photonic Crystal Calculations. Part 2: Properties and Implementation
,”
J. Opt. Soc. Am.
,
A17
, pp.
2177
–
2190
.
Copyright © 2003
 by ASME
You do not currently have access to this content.