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Research Papers

Topology Optimized Cloak for Airborne Sound

[+] Author and Article Information
Jacob Andkjær

e-mail: jban@mek.dtu.dk

Ole Sigmund

e-mail: sigmund@mek.dtu.dk
Department of Mechanical Engineering,
Technical University of Denmark,
2800 Kgs. Lyngby, Denmark

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 30, 2012; final manuscript received September 7, 2012; published online June 6, 2013. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 135(4), 041011 (Jun 06, 2013) (5 pages) Paper No: VIB-12-1137; doi: 10.1115/1.4023828 History: Received April 30, 2012; Revised September 07, 2012

Directional acoustic cloaks that conceal an aluminum cylinder for airborne sound waves are presented in this paper. Subwavelength cylindrical aluminum inclusions in air constitute the cloak design to aid practical realizations. The positions and radii of the subwavelength cylinders are determined by minimizing scattering from the cloak-structure and cylinder using the gradient-based topology optimization method. In the final optimization step, the radii of the subwavelength cylinders are constrained to three discrete values. A near-perfect narrow-banded and angular cloaking effect is obtained by optimizing for one target frequency. To get a larger bandwidth, the acoustic cloak is optimized for three frequencies at the cost of reduced peak cloaking performance at the center frequency.

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Figures

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Fig. 2

A uniform pressure wave (a) incident on an aluminum cylinder (b) generate a significant amount of scattering, especially behind the cylinder

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Fig. 1

Schematics of a cylindrical cloak that conceals an aluminum cylinder for a uniform pressure wave in air. The position and radius of each aluminum rod can be varied continuously in the design domain Ωdes to create the cloaking effect of the big aluminum cylinder.

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Fig. 4

Optimized design of an acoustic cloak with 78 cylindrical aluminum inclusions in air is shown in (a). The radii of all cylinders are constrained to take discrete values of either 0.5 cm, 1.0 cm, or 1.5 cm to aid realizations. Near-perfect cloaking is obtained with the optimized cylinder placement, as seen from (b). The combined scattering pattern from the optimized subwavelength structures cancels the scattering from the big cylinder by a resonance effect.

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Fig. 5

Cloaking performance, as a function of the incident angle, on the scattering cylindrical object wrapped in the acoustic cloaking structure from Fig. 4. An incident angle of 0 degrees corresponds to an incident wave propagating in a direction parallel to the x-axis and 90 degrees parallel to the y-axis.

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Fig. 3

A three-step MMOS-based optimization approach for acoustic cloak design. (a) Initial design with 306 aluminum cylinders. (b) Optimized design, where the cylinders can change in size and position. (c) Cylinders with a radius smaller than 0.25 cm are discarded. (d) Design after reoptimizing with a lower bound on the radii. (e) Radii of all cylinders are rounded off to 0.5 cm, 1.0 cm, or 1.5 cm. (f) Final design after reoptimizing the positions of the cylinders.

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Fig. 6

The bandwidth is very narrow for an acoustic cloak (a) optimized for one target frequency (4367 Hz). The bandwidth can be broadened for a cloak (b) optimized for three frequencies (4326 Hz, 4367 Hz, and 4408 Hz) at the cost of reduced cloaking performance at the center frequency (4367 Hz). The circular markers show the cloaking performances at the target frequencies.

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