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Research Papers

Elastic Wave Localization in Layered Phononic Crystals With Fractal Superlattices

[+] Author and Article Information
Zhi-zhong Yan

School of Mathematics,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: zzyan@bit.edu.cn

Chuanzeng Zhang

Department of Civil Engineering,
University of Siegen,
Siegen D-57068, Germany

Yue-sheng Wang

Institute of Engineering Mechanics,
Beijing Jiaotong University,
Beijing 100044, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 31, 2012; final manuscript received October 19, 2012; published online June 6, 2013. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 135(4), 041004 (Jun 06, 2013) (8 pages) Paper No: VIB-12-1024; doi: 10.1115/1.4023818 History: Received January 31, 2012; Revised October 19, 2012

In this paper, localization phenomena of in-plane time-harmonic elastic waves propagating in layered phononic crystals (PNCs) with different fractal superlattices are studied. For this purpose, oblique wave propagation in layered structures is considered. To describe wave localization phenomena, the localization factor is applied and computed by the transfer matrix method. Three typical fractal superlattices are considered, namely, the Cantorlike fractal superlattice (CLFSL), the golden-section fractal superlattice (GSFSL), and the Fibonacci fractal superlattice (FFSL). Numerical results for the localization factors of CLFSL, GSFSL, and FFSL are presented and analyzed. The results show that the localization factor of a CLFSL exhibits an approximate similarity and band-splitting properties. The number of decomposed bandgaps of the GSFSL and FFSL follows the composition of the special fractal structures. In addition, with increasing fractal series, the value of the localization factor is enlarged. These results are of great importance for structure design of fractal PNCs.

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Figures

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Fig. 4

Localization factors versus the normalized frequency and the incidence angle in the gray-scale map for (a) S = 1 and (b) S = 2

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Fig. 3

Localization factors for in-plane waves propagating normally in CLFSL with generator G = BAB and series S ranging from 1 to 3

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Fig. 6

Localization factors for in-plane waves propagating normally in GSFSL with series S ranging from 1 to 3

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Fig. 5

Structures of GSFSL

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Fig. 8

Structures of FFSL

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Fig. 7

Localization factors versus the normalized frequency and the incidence angle in the gray-scale map for (a) S = 1 and (b) S = 2

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Fig. 9

Localization factors for in-plane waves propagating normally in two-periodic FFSL with series S ranging from 3 to 6

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Fig. 10

Localization factors versus the normalized frequency and the incidence angle in the gray-scale map for (a) S = 3 and (b) S = 4

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Fig. 11

Localization factors for in-plane waves propagating normally in fourth series FFSL with a period p ranging from 2 to 5

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Fig. 2

Structures of CLFSL with generator G = BAB

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Fig. 1

A schematic diagram of a layered PNC

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