The study of periodic media, including periodic materials and structures, has a long history in the field of vibrations and acoustics. Origins can be traced back to Newton's first attempt to formulate the motion of sound in air [1] and Rayleigh's study of continuous periodic structures [2]. The topic has grown to become of fundamental importance in condensed matter physics due to the role that atomic vibrations play in determining the properties of crystals [3,4]. The engineering discipline, for its part, has contributed significantly to advancing the field through development of analytical, computational, and experimental analysis techniques applied to composite materials, multistory buildings, multispan bridges, multiblade turbines, ribbed plates and shells in aerospace and marine structures, MEMS arrays, etc. [5].

In recent years, the topic has experienced a resurgence with the introduction of phononic crystals...

References

References
1.
Newton
,
I.
,
1686
, Philosophiæ Naturalis Principia Mathematica, Cambridge Digital Library, Cambridge, UK, http://cudl.lib.cam.ac.uk/view/PR-ADV-B-00039-00001
2.
Rayleigh
,
J. W. S.
,
1887
, “
On the Maintenance of Vibrations by Forces of Double Frequency and on the Propagation of Waves Through a Medium Endowed with a Periodic Structure
,”
Philos. Mag.
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24
, pp.
145
159
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3.
Bloch
,
F.
,
1928
, “
Über die Quantenmechanik der Electron in Kristallgittern
,”
Z. Phys.
,
52
, pp.
555
600
.
4.
Brillouin
,
L.
,
1953
,
Wave Propagation in Periodic Structures
,
2nd ed.
,
Dover
,
New York
.
5.
Mead
,
D. J.
,
1996
, “
Wave Propagation in Continuous Periodic Structures: Research Contributions from Southampton
,”
J. Sound Vib.
,
190
, pp.
495
524
.
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