Within periodically heterogeneous materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. A novel multiscale dispersive design methodology is presented by which periodic unit cells are designed for desired frequency band structures, and are used as building blocks for forming fully or partially periodic structures, typically at larger length scales. Structures resulting from this hierarchical design approach are tailored to desired dynamical characteristics without the necessity for altering the overall geometric shape of the structure nor employing dissipative damping materials. Case studies are presented for shock isolation and frequency sensing.

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
,”
J. Computational Physics
,
158
, pp.
214
224
.
4.
Ruzzene
M.
and
Scarpa
F.
,
2005
, “
Directional and Band-Gap Behanior of Auxetic Lattices
,”
Physica Status Solidi B
,
242
, No.
3
, pp.
695
709
.
5.
Cai, L.-W., 2004, “Tunable Phononic Band Gap Crystal Using Eccentric Multilayered Scatterers,” Proc. of the 2004 ASME International Mechanical Engineering Congress and R&D Expo, Anaheim, California, [IMECE2004-59671].
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.
Diaz
A. R.
and
Kikuchi
N.
,
1992
, “
Solutions to Shape and Topology Eigenvalue Optimization Problems Using a Homogenization Method
,”
International Journal for Numerical Methods in Engineering
,
35
, No.
7
, pp.
1487
1502
.
8.
Ma
Z.-D.
,
Kikuchi
N.
, and
Cheng
H.-C.
,
1995
, “
Topological Design for Vibrating Structures
,”
Computer Methods in Applied Mechanics and Engineering
,
121
, No.
1–4
, pp.
259
280
.
9.
Zhao
C. B.
,
Steven
G. P.
, and
Xie
Y. M.
,
1997
, “
Evolutionary Optimization of Maximizing the Difference Between Two Natural Frequencies of a Vibrating Structure
,”
Structural Optimization
,
13
, No.
2–3
, pp.
148
154
.
10.
Lai
E.
and
Ananthasuresh
G. K.
,
2002
, “
On the Design of Bars and Beams for Desired Mode Shapes
,”
Journal of Sound and Vibration
,
254
, No.
2
, pp.
393
406
.
11.
Hussein, M.I., Hulbert, G.M., and Scott, R.A., 2003, “Band-Gap Engineering of Elastic Wave Guides Using Periodic Materials,” Proc. of the 2003 ASME International Mechanical Engineering Congress and R&D Expo, Washington, D.C., pp. 799–807 [IMECE2003-41886].
12.
Hussein, M.I., “Dynamics of Banded Materials and Structures: Analysis, Design and Computation in Multiple Scales,” Ph.D. Thesis, University of Michigan, Ann Arbor, Michigan, 2004.
13.
Hussein, M.I., Hulbert, G.M., and Scott, R.A., 2005 “Dispersive Elastodynamics of ID Banded Materials and Structures: Analysis,” Journal of Sound and Vibration, in press.
14.
Hussein, M.I., Hulbert, G.M. and Scott, R.A., 2002 “Tailoring of Wave Propagation Characteristics in Periodic Structures with Multilayer Unit Cells.” Proc. of the 7th American Society of Composites Technical Conference, West Lafayette, Indiana, [CD ROM: pp. 1–9].
15.
Floquet
G.
,
1883
,
Sur les E´quations Diffe´rentielles Linearies a` Coefficients Pe´riodiques
,”
Ann. E´cole Norm
,
12
, pp.
47
88
.
16.
Esquivel-Sirvent
R.
and
Cocoletzi
G. H.
,
1994
, “
Band-structure for the Propagation of Elastic-waves in Superlattices
,”
J. of the Acoustical Society of America
,
95
, No.
1
, pp.
86
90
.
17.
Shen
M. R.
and
Cao
W. W.
,
2000
, “
Acoustic Bandgap Formation in a Periodic Structure with Multilayer Unit Cells
,”
J. of Physics D-Applied Physics
,
33
, No.
10
, pp.
1150
1154
.
18.
Hussein, K. Hamza, K., Hulbert, G.M., Scott, R.A., and Saitou, S., “Multi-Objective Evolutionary Optimization of Periodic Layered Materials for Desired Wave Dispersion Characteristics,” Structural and Multidisciplinary Optimization, in press.
This content is only available via PDF.
You do not currently have access to this content.