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Research Papers

A Two-Way Unidirectional Narrow-Band Acoustic Filter Realized by a Graded Phononic Crystal

[+] Author and Article Information
Yingjie Chen

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China

Yang Huang

Department of Civil Engineering,
Zhejiang University,
Hangzhou 310058, China
e-mail: 0015818@zju.edu.cn

Chaofeng Lü

Department of Civil Engineering,
Zhejiang University,
Hangzhou 310058, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China;
Soft Matter Research Center,
Zhejiang University,
Hangzhou 310027, China

Weiqiu Chen

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China;
Soft Matter Research Center,
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of Fluid Power
and Mechatronic Systems,
Zhejiang University,
Hangzhou 310027, China

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 25, 2017; final manuscript received June 19, 2017; published online July 7, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(9), 091003 (Jul 07, 2017) (6 pages) Paper No: JAM-17-1275; doi: 10.1115/1.4037148 History: Received May 25, 2017; Revised June 19, 2017

Unidirectional acoustic transmission is acquired in a one-dimensional graded phononic crystal. The distinct feature of the present design is that waves can propagate unidirectionally at a certain frequency from the left to right, and waves at another frequency can propagate in the opposite direction from the right to left. This two-way asymmetric propagation behavior is realized at the narrow resonant frequencies in the acoustic band gap by a novel mechanism, which is totally linear and obeys the time-reversal symmetry. Simulation shows that for the graded heterogeneous structure, the resonant peaks of frequency in the acoustic band gap for opposite propagation directions become different. In the transmission spectrum, this mechanism corresponds to a pass-band splitting, and each separated peak represents a unidirectional propagation behavior. The separation of two peaks has been proved to have a close relation to the grading degree of the material property in the spatially periodic components. The unique propagation characteristic obtained at resonant frequencies in the band gaps may provide us a new way to realize a two-way unidirectional narrow-band acoustic filter.

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Figures

Grahic Jump Location
Fig. 1

Sketch of the finite periodic structure with grading property

Grahic Jump Location
Fig. 2

(a) Band structure of an infinite periodic structure and (b) transmission spectrum of a finite periodic structure

Grahic Jump Location
Fig. 3

Transmission spectra for different KA and uniform material B: (a) KA = 0.01, (b) KA = 0.02, and (c) KA = 0.03

Grahic Jump Location
Fig. 4

Transmission spectra for the same KA = 0.02 and different KB: (a) KB = 0.02, (b) KB = 0, and (c) KB = −0.02

Grahic Jump Location
Fig. 5

Separation of resonant peaks as a function of KA + KB with the constraint conditions: (a) KB = 0, (b) KA = 0, and (c) KA = KB

Grahic Jump Location
Fig. 6

Natural frequencies of the structure (KA = 0.02 and KB = 0) with different boundary conditions: (a) left-hand side fixed and right-hand side free and (b) left-hand side free and right-hand side fixed

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