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Research Papers

Formation of Bending-Wave Band Structures in Bicoupled Beam-Type Phononic Crystals

[+] Author and Article Information
Y. Q. Guo

Key Laboratory of Mechanics on Disaster
and Environment in Western China,
Ministry of Education,
School of Civil Engineering and Mechanics,
Lanzhou University,
Lanzhou 730000, China
e-mail: guoyq@lzu.edu.cn

D. N. Fang

State Key Laboratory of Turbulence
and Complex Systems,
College of Engineering,
Peking University,
Beijing 100871, China

Manuscript received February 7, 2013; final manuscript received March 13, 2013; accepted manuscript posted March 21, 2013; published online August 22, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(1), 011009 (Aug 22, 2013) (17 pages) Paper No: JAM-13-1065; doi: 10.1115/1.4024076 History: Received February 07, 2013; Revised March 13, 2013; Accepted March 21, 2013

Beam-type phononic crystals as one kind of periodic material bear frequency bands for bending waves. For the first time, this paper presents formation mechanisms of the phase constant spectra in pass-bands of bending waves (coupled flexural and thickness-shear waves) in bicoupled beam-type phononic crystals based on the model of periodic binary beam with rigidly connected joints. Closed-form dispersion relation of bending waves in the bicoupled periodic binary beam is obtained by our proposed method of reverberation-ray matrix (MRRM), based on which the bending-wave band structures in the bicoupled binary beam phononic crystal are found to be generated from the dispersion curves of the equivalent bending waves in the unit cell due to the zone folding effect, the cut-off characteristic of thickness-shear wave mode, and the wave interference phenomenon. The ratios of band-coefficient products, the characteristic times of the unit cell and the characteristic times of the constituent beams are revealed as the three kinds of essential parameters deciding the formation of bending-wave band structures. The MRRM, the closed-form dispersion relation, the formation mechanisms, and the essential parameters for the bending-wave band structures in bicoupled binary beam phononic crystals are validated by numerical examples, all of which will promote the applications of beam-type phononic crystals for wave filtering/guiding and vibration isolation/control.

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Figures

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Fig. 1

Schematic and description of the unit cell of an infinite 1D bicoupled binary beam phononic crystal. (a) The schematic of the unit cell. (b) The global and local coordinates. (c) Sign convention for the generalized displacements and forces. (d) Convention for the wave amplitudes of flexural and thickness-shear modes.

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Fig. 2

The incident and the reflected waves at joints and the propagating waves in component beams of the unit cell

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Fig. 3

The lowest three phase and attenuation constant spectra of bending waves in the bicoupled binary-I beam phononic crystal by our analysis and their comparison with those by the TMM

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Fig. 4

The comparison of first several bending-wave band structures in the four exemplified bicoupled periodic binary beams

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Fig. 5

The band structures within ωωcmin of bending waves in the exemplified bicoupled binary-IV beam phononic crystal

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Fig. 6

The band structures within ωcmin < ωωcmax of bending waves in the exemplified bicoupled binary-IV beam phononic crystal

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Fig. 7

The band structures in ω > ωcmax (260 kHz ≤ ω ≤ 370 kHz) of bending waves in the exemplified bicoupled binary-IV beam phononic crystal

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Fig. 8

The alterations of bending-wave band structures with the characteristic times of unit cell as the constituent beams are identical in bicoupled binary beam phononic crystals

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Fig. 9

The alterations of bending-wave band structures with the ratios of band-coefficient products in bicoupled binary beam phononic crystals

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Fig. 10

The alterations of bending-wave band structures with the characteristic times of constituent beams in bicoupled binary beam phononic crystals

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