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Research Papers

Two-Dimensional Arbitrarily Shaped Acoustic Cloaks With Triangular Patterns of Homogeneous Properties

[+] Author and Article Information
Qi Li

Department of Mechanical Engineering and
Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261;
Naval Architecture and Ocean Engineering
College,
Dalian Maritime University,
Dalian 116026, China

Jeffrey S. Vipperman

Department of Mechanical Engineering and
Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261
e-mail: jsv@pitt.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 4, 2018; final manuscript received October 24, 2018; published online November 30, 2018. Assoc. Editor: Stefano Gonella.

J. Vib. Acoust 141(2), 021014 (Nov 30, 2018) (7 pages) Paper No: VIB-18-1241; doi: 10.1115/1.4041897 History: Received June 04, 2018; Revised October 24, 2018

Acoustic cloaking is an intriguing phenomenon that has attracted lots of attention. The required inhomogeneous and anisotropic properties of acoustic cloaks derived with transformation acoustics make them difficult to realize. In this paper, a new mapping relation is presented. An acoustic cloak can be divided into any number of arbitrary triangular patterns, which are mapped from similar patterns in virtual space. Transformation from one triangular domain to another leads to homogeneous properties using transformation acoustics. The resulting cloak is composed of homogeneous triangular parts, each having just two alternating layers of material. The manner of division of the cloak affects the properties of each triangular part dramatically, which can be leveraged to vary the properties of each triangular part for more realistic material properties. Simulations of models based on this method show good cloaking performance at reducing the reflected and scattered waves due to the cloaked obstacle.

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Figures

Grahic Jump Location
Fig. 1

Transformation from virtual space (Ω) to physical space (ω) with similar patterns

Grahic Jump Location
Fig. 2

Sample transformation from a triangle in virtual space to one in physical space

Grahic Jump Location
Fig. 3

Mapping of a section with three triangles

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Fig. 4

Variation of effective (a) densities and (b) bulk moduli as coefficients α and β are varied (δ1 = δ2 = 0.05 and γ1 = γ2 = 0.5)

Grahic Jump Location
Fig. 5

Variation of effective sound speeds as coefficients α and β are varied (δ1 = δ2 = 0.05 and γ1 = γ2 = 0.5)

Grahic Jump Location
Fig. 6

Approximate circular cloak with sections of three homogeneous parts built with layered structures

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Fig. 7

The pressure field for a plane wave with amplitude of 1 Pa: (a) without cloak and (b) with circular cloak

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Fig. 8

Normalized amplitude of the scattered waves at r = 5λ

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Fig. 9

Reduced total RCS of the cloak

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Fig. 10

Mapping of a section with five triangles

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Fig. 11

The pressure field for a plane wave with amplitude of 1 Pa: (a) without cloak, direction 1, (b) with the square cloak, direction 1, (c) without cloak, direction 2, and (d) with the square cloak, direction 2

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