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Research Papers

Wave Energy Focalization in a Plate With Imperfect Two-Dimensional Acoustic Black Hole Indentation

[+] Author and Article Information
Wei Huang

State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Yudao Street 29,
Nanjing 210016, China
e-mail: huangwei91@nuaa.edu.cn

Hongli Ji

State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Yudao Street 29,
Nanjing 210016, China;
Department of Mechanical Engineering,
Hong Kong Polytechnic University,
Hung Hom,
Kowloon 999077, Hong Kong
e-mail: jihongli@nuaa.edu.cn

Jinhao Qiu

Fellow ASME
State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Yudao Street 29,
Nanjing 210016, China
e-mail: qiu@nuaa.edu.cn

Li Cheng

Department of Mechanical Engineering,
Hong Kong Polytechnic University,
Hung Hom,
Kowloon 999077, Hong Kong
e-mail: li.cheng@polyu.edu.hk

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 8, 2015; final manuscript received June 24, 2016; published online August 8, 2016. Assoc. Editor: Miao Yu.

J. Vib. Acoust 138(6), 061004 (Aug 08, 2016) (12 pages) Paper No: VIB-15-1512; doi: 10.1115/1.4034080 History: Received December 08, 2015; Revised June 24, 2016

The acoustic black hole (ABH) phenomenon in thin-walled structures with a tailored power-law-profiled thickness allows for a gradual change of the phase velocity of flexural waves and energy focalization. However, ideal ABH structures are difficult to realize and suffer from potential structural problems for practical applications. It is therefore important to explore alternative configurations that can eventually alleviate the structural deficiency of the ideal ABH structures, while maintaining similar ability for wave manipulation. In this study, the so-called imperfect two-dimensional ABH indentation with different tailored power-law-profiled is proposed and investigated. It is shown that the new indentation profile also enables a drastic increase in the energy density around the tapered area. However, the energy focalization phenomena and the process are shown to be different from those of conventional ABH structure. With the new indentation profile, the stringent power-law thickness variation in ideal ABH structures can be relaxed, resulting in energy focalization similar to a lens. Different from an ideal ABH structure, the energy focalization point is offset from, and downstream of indentation center, depending on the structural geometry. Additional insight on energy focalization in the indentation is quantitatively analyzed by numerical simulations using structural power flow. Finally, the phenomenon of flexural wave focalization is verified by experiments using laser ultrasonic scanning technique.

Copyright © 2016 by ASME
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Figures

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Fig. 1

Plate with a nonideally profiled ABH indentation ((a) and (b)), amplitude of five-period Hanning-windowed tone burst force (c), and normal drive position indicated (d)

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Fig. 2

Displacement at 10 kHz of plates: (a) with a uniform thickness and (b) with a variable thickness

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Fig. 3

Displacement at 10 kHz of plates: (a) the imperfect ABH (h=ε(r−r1)m+h1,m=2) and (b) the conventional ABH (h=εrm,m=2)

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Fig. 4

Sum of squared displacement at f = 5 kHz (a) and f = 10 kHz (b) for plates with m=2,r1=0.02 m, and h1=0.001 m

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Fig. 5

Results of the energy distribution on the plate for (a) the displacement response and (b) the energy distribution

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Fig. 6

Energy distribution at different cross sections and spots: (a) and (b) at T=1.1τ and (c) and (d) at T=1.3τ

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Fig. 7

The influence of the power-law function of thickness onthe position of energy focalization for r1=0.02 m andh1=0.001 m

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Fig. 8

The refractive index gradient from r2 to r1 for m=2, m=3, and m=4

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Fig. 9

Simulated displacement of plates for r1=0.02 m and h1=0.001 m : (a) m=1 and (b) m=1.5

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Fig. 10

The influence of the thickness of the central circular plateau on the position of energy focalization with r1=0.02 m

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Fig. 11

The refractive index gradient from r2 to r1 for h1=0.0005 m, h1=0.001 m, h1=0.0015 m, and h1=0.002 m

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Fig. 12

The influence of the radius of circular plate on the focal position of energy focalization with h1=0.001 m

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Fig. 13

The graded refractive index gradient for r1=0.005 m, r1=0.01 m, r1=0.015 m, and r1=0.02 m

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Fig. 14

Variation of focal position of energy focalization with the index m for different frequencies (f = 5 kHz and f = 10 kHz) with r1=0.02 m and h1=0.001 m

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Fig. 15

Vector field of power flow in plate: (a) plate with r1=0.02 m and h1=0.0005 m, (c) plate with r1=0.02 m and h1=0.001 m, and (b) and (d) enlarged images for a quarter of (a) and (c)

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Fig. 16

Vector field of power flow in plate: (a) plate with m=2,r1=0.02 m, and h1=0.001 m and (b) plate with m=3,r1=0.02 m, and h1=0.001 m

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Fig. 17

Temporal change of power flow at different sections on the plate with m=2,r1=0.02 m, and h1=0.001 m

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Fig. 18

The influence of index m on power flow with r1=0.02 m and h1=0.001 m : (a) temporal change of power flow at section 2 and (b) ratio of the power flow at section 2 to the power flow at section 1

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Fig. 19

The influence of index m on the power flow with r1=0.02 m and h1=0.001 m: (a) temporal change of power flow at section 3 and (b) ratio of the power flow at section 3 to the power flow at section 1

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Fig. 20

Experimental system: (a) schematic diagram of the laser ultrasonic system and (b) experimental setup of the laser ultrasonic scanning system

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Fig. 21

Diagrammatic sketch of experimental plate

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Fig. 22

The wavefields for d = 150 mm: (a) and (b) simulated wavefields at different times and (c) and (d) experimental wavefields at corresponding time

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Fig. 23

The normalized wave energy distribution: (a) simulated result and (b) experimental result

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