A phononic material is commonly characterized by its dispersive frequency spectrum. With appropriate spatial distribution of the constituent material phases, spectral stop bands could be generated. Moreover, it is possible to control the number, the width, and the location of these bands within a frequency range of interest. This study aims at exploring the relationship between the unit cell configuration and its frequency spectrum characteristics. Focusing on 1D layered phononic materials, and longitudinal wave propagation in the direction normal to the layering, the unit cell features of interest are the number of layers and the material phase and relative thickness of each layer. An evolutionary search for multi-phase cell designs exhibiting a wide stop band, or a series of wide stop bands, is conducted using a specially formulated representation and set of operators that break the symmetries in the problem. An array of optimal designs for a range of ratios in Young's modulus and density are obtained and the corresponding objective values are plotted as a function of the ratios of the phase properties. Structures composed of the designed phononic materials are excellent candidates for use in a wide range of applications including vibration and sound isolation.

1.
Sigmund
O.
and
Jensen
J. S.
,
2003
, “
Systematic Design of Phononic Band-Gap Materials and Structures by Topology Optimization
,”
Philosophical Transactions Royal Society of London A
,
361
, pp.
1001
1019
.
2.
Cox
S. J.
and
Dobson
D. C.
,
1999
, “
Maximizing Band Gaps in Two Dimensional Photonic Crystals
,”
SIAM J. Applied Mathematics
,
59
, pp.
2108
2120
.
3.
Cox
S. J.
and
Dobson
D. C.
,
2000
, “
Band Structure Optimization of Two Dimensional Photonic Crystals in H-Polarization
,”
Journal of Computational Physics
,
158
, pp.
214
224
.
4.
Hussein
M. I.
,
Hamza
K.
,
Hulbert
G. M.
,
Scott
R. A.
, and
Saitou
S.
,
2006
, “
Multi-Objective Evolutionary Optimization of Periodic Layered Materials for Desired Wave Dispersion Characteristics
,”
Structural and Multi-disciplinary Optimization
,
31
, pp.
60
75
.
5.
Hussein, M.I. Hamza, K., Hulbert, G.M., Scott, R.A., and Saitou, S., 2004, “Evolutionary Topology Optimization of Periodic Materials for Vibration and Shock Isolation,” Proc. of the 8th International Conference on Production Engineering, Design and Control, Alexandria University, Alexandria, Egypt, December 2004, [CD ROM: pp. 1–10].
6.
Burger
M.
,
Osher
S. J.
and
Yablonovitch
E.
,
2004
, “
Inverse Problem techniques for the design of photonic crystals
,”
IEICE Transactions on Electronics
,
E87C
, pp.
258
265
.
7.
Ruzzene
M.
and
Scarpa
F.
,
2005
, “
Directional and Band-Gap Behanior of Auxetic Lattices
,”
Physica Status Solidi B
,
242
, No.
3
, pp.
695
709
.
8.
Rupp, C., Frenzel, M., Evgrafov, A., Maute, K. and Dunn, M.L., “Design of Nanostructured Phononic Materials,” Proc. of the 2005 ASME International Mechanical Engineering Congress and R&D Expo, Orlando, Florida, November 2005, [CD ROM: pp. 1–6], [IMECE2005-82206].
9.
Hussein, M.I., Hulbert, G.M. and Scott, R.A., “Hierarchical Design of Phononic Materials and Structures,” Proc. of the 2005 ASME International Mechanical Engineering Congress and R&D Expo, Orlando, Florida, November 2005, [CD ROM: pp. 1–10], [IMECE2005-81325].
10.
El-Beltagy, M.A. and Hussein, M.I., “Evolutionary Scale-Preserving and Repair-Free Operators for the Design of Layered Composite Materials for Vibration and Shock Isolation,” Proc. of the 7th International Conference on Production Engineering and Design for Development, Ain Shams University, Cairo, Egypt, February 2006, pp. 277–287.
11.
Esquivel-Sirvent
R.
and
Cocoletzi
G. H.
,
1994
, “
Band-structure for the Propagation of Elastic-waves in Superlattices
,”
Journal of the Acoustical Society of America
,
95
, No.
1
, pp.
86
90
.
12.
Hussein
M. I.
,
Hulbert
G. M.
and
Scott
R. A.
,
2006
Dispersive Elastodynamics of 1D Banded Materials and Structures: Analysis
,”
J. of Sound and Vibration
,
289
, pp.
779
806
.
13.
Goldberg, D., Genetic Algorithms in Search Optimization and Machine Learning, Addison-Wesley, 1989.
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