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Research Papers

Alternative Designs of Acoustic Lenses Based on Nonlinear Solitary Waves

[+] Author and Article Information
Kaiyuan Li

Laboratory for Nondestructive Evaluation
and Structural Health Monitoring Studies,
Department of Civil
and Environmental Engineering,
University of Pittsburgh,
3700 O'Hara Street,
Pittsburgh, PA 15261

Piervincenzo Rizzo

Laboratory for Nondestructive Evaluation
and Structural Health Monitoring Studies,
Department of Civil
and Environmental Engineering,
University of Pittsburgh,
3700 O'Hara Street,
Pittsburgh, PA 15261
e-mail: pir3@pitt.edu

Xianglei Ni

INTECSEA, WorleyParsons Group,
Floating System Department,
575 N. Dairy Ashford,
Houston, TX 77079

1Corresponding author.

Manuscript received January 7, 2014; final manuscript received March 31, 2014; accepted manuscript posted April 2, 2014; published online April 25, 2014. Assoc. Editor: John Lambros.

J. Appl. Mech 81(7), 071011 (Apr 25, 2014) (9 pages) Paper No: JAM-14-1018; doi: 10.1115/1.4027327 History: Received January 07, 2014; Revised March 31, 2014; Accepted April 02, 2014

In the last decade, there has been an increasing attention on the use of highly- and weakly-nonlinear solitary waves in engineering and physics. These waves can form and travel in nonlinear systems such as one-dimensional chains of particles. When compared to linear elastic waves, solitary waves are much slower, nondispersive, and their speed is amplitude-dependent. Moreover, they can be tuned by modifying the particles' material or size, or the chain's precompression. One interesting engineering application of solitary waves is the fabrication of acoustic lenses, which are employed in a variety of fields ranging from biomedical imaging and surgery to defense systems and damage detection in materials. In this paper, we propose the design of acoustic lenses composed by one-dimensional chains of spherical particles arranged to form a line or a circle array. We show, by means of numerical simulations and an experimental validation, that both the line and circle arrays allow the focusing of waves transmitted into a solid or liquid (the host media) and the generation of compact sound bullets of large amplitude. The advantages and limitations of these nonlinear lenses to attain accurate high-energy acoustic pulses with high signal-to-noise ratio are discussed.

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Figures

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Fig. 1

Schematics of the wave field generated in a linear medium by a line array made of n chains made of spherical particles

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Fig. 2

Alternative design of line arrays. Center-to-center distance of chains 1,2,…,10 from the central chain as a (a) function of the dynamic contact force and (b) function of the velocity of the strikers.

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Fig. 3

Schematics of a circle array made of 21 chains of 9.525 mm diameter particles. In order to carry a direct comparison between this array and the line arrays described earlier, D = 64.5 mm and d = 9.65 mm. Drawing not to scale.

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Fig. 4

Dynamic contact forcing function on the interface between the last beads of line array HNSW transducers and the polycarbonate media. The curves denote the forcing function between the media and the last beads from the middle chain to the right chain, with the peaks from the right to the left, respectively.

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Fig. 5

Designs of a line array and circle array made of 21 chains of particles. Von Mises stress in polycarbonate with line array lens at (a) 290 μs (c) 310 μs (e) 342 μs. Von Mises stress in polycarbonate with circle array lens at (b) 290 μs (d) 310 μs (f) 346 μs.

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Fig. 6

Maximum von Mises stress as a function of the depths

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Fig. 7

Designs of a line array and circle array made of 21 chains of particles. Pressure field generated by the line array lens with differential precompression in water at (a) 350 μs (c) 360 μs and (e) 368 μs. Pressure field generated by the circle array lens in water at (b) 350 μs (d) 360 μs (f) 372 μs.

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Fig. 8

Pressure versus time plot at the focal point which is 100 mm (a) under the middle chain of the line array under the FSI on the axis of the circle array. (b) Comparison between the line array and circle array for the maximum pressure amplitude along the lens axis.

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Fig. 9

Top and elevation view of the experimental lens

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Fig. 10

The experimental setup. (a) Scheme of the horizontal and vertical scanning lines and (b) photo of the entire setup.

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Fig. 11

(a) Time waveform and associated (b) Gabor wavelet transform of a signal recorded 50 mm underneath the fluid structure interface at the axis of symmetry

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Fig. 12

Normalized maximum pressure amplitude of both experimental and FEM results along the scanning lines (a) H and (b) V

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