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Transformation Media in Acoustics with Constant Bulk Modulus or Constant Density Tensor

Published online by Cambridge University Press:  19 August 2015

Y.-L. Tsai  and
T. Chen
Y.-L. Tsai
Affiliation:
Department of Civil EngineeringNational Cheng Kung UniversityTainan, Taiwan
T. Chen*
Affiliation:
Department of Civil EngineeringNational Cheng Kung UniversityTainan, Taiwan
*
*Corresponding author (tchen@mail.ncku.edu.tw)
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Abstract

This work is to present a formulation of cloaking or concentrating device in acoustics in which the transformed material could be either having uniform bulk modulus or having homogeneous density tensor. The transformed material parameters, depending on the mapping of physical and virtual coordinates, are often position-varying and anisotropic. This often adds substantial complexity in practical implementation. Here we present a theoretical algorithm that allows us to design a transformation field that could have either uniform bulk modulus or constant density tensor. For cloaking devices with constant bulk modulus, analytical and numerical results are presented for circular as well as for non-circular cloaking devices. Specifically, elliptical and twin-cloak devices are exemplified. To achieve the effect of constant density tensor, we consider only circular geometry. Devices with cloaking or concentrating effects can be exactly formulated. We note, however, that it seems unlikely at this moment to have a transformation device that has constant bulk modulus and constant density tensor at the same time. Nevertheless, we remark the present results are of still sufficient merit in that the uniform material parameters, in either set of material parameters, indeed greatly simplify the practice in real implementations.

Keywords

Transformation acousticsCloakConstant material parameters
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 3 , June 2016 , pp. 313 - 323
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2016 

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References

1.Pendry, J. B., Schurig, D. and Smith, D. R., “Controlling Electromagnetic Fields,” Science, 312, pp. 1780–1782 (2006).Google Scholar
2.Leonhardt, U., “Optical Conformal Mapping,” Science, 312, pp. 1777–1780 (2006).Google Scholar
3.Rahm, M., Schurig, D., Roberts, D. A., Cummer, S. A., Smith, D. R. and Pendry, J. B., “Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwells Equations,” Photonics and Nano structures-Fundamentals and Applications, 6, pp. 87–95 (2008).Google Scholar
4.Chen, H. Y. and Chan, C. T., “Transformation Media that Rotate Electromagnetic Fields,” Applied Physics Letters, 90, p. 241105 (2007).Google Scholar
5.Chen, H. Y., Hou, B., Chen, S., Ao, X., Wen, W. and Chan, C. T., “Design and Experimental Realization of a Broadband Transformation Media Field Rotator at Microwave Frequencies,” Physics Review Letters, 102, p. 183903 (2009).Google Scholar
6.Rahm, M., Cummer, S. A., Shurig, D., Pendry, J. B. and Smith, D. R., “Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations,” Physics Review Letters, 100, p. 063903 (2008).Google Scholar
7.Chen, H. Y. and Chan, C. T., “Electromagnetic Wave Manipulation by Layered Systems Using the Transformation Media Concept,” Physics Review B, 78, p. 054204 (2008).CrossRefGoogle Scholar
8.Milton, G. W., Briane, M. and Willis, J. R., “On Cloaking for Elasticity and Physical Equations with a Transformation Invariant Form,” New Journal of Physics, 8, p. 248 (2006).Google Scholar
9.Cummer, S. A. and Schurig, D., “One Path to Acoustic Cloaking,” New Journal of Physics, 9, p. 45 (2007).CrossRefGoogle Scholar
10.Chen, H. Y. and Chen, C. T., “Acoustic Cloaking in Three Dimensions Using Acoustic Metamaterials,” Applied Physics Letters, 91, p. 183518 (2007).Google Scholar
11.Cai, L.-W. and Sánchez-Dehesa, J., “Analysis of Cummer-Schurig Acoustic Cloaking,” New Journal of Physics, 9, p. 450 (2007).CrossRefGoogle Scholar
12.Cummer, S. A., Popa, B.-I., Schurig, D., Smith, D. R., Pendry, J. B., Rahm, M. and Starr, A., “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell,” Physics Review Letters, 100, p. 024301 (2008).Google Scholar
13.Farhat, M., Guenneau, S., Enoch, S. and Movchan, A. B., “Cloaking Bending Waves Propagating in Thin Elastic Plates,” Physics Review B, 79, p. 033102 (2009).Google Scholar
14.Zhang, S., Xia, C. and Fang, N., “Broadband Acoustic Cloak for Ultrasound Wave,” Physics Review Letters, 106, p. 024301 (2011).Google Scholar
15.Sanchis, L., Garcia-Chocano, V. M., Llopis-Pontiveros, R., Climente, A., Martinez-Pastor, J., Cervera, F. and Sánchez-Dehesa, J., “Three-Dimensional Axisymmetric Cloak Based on the Cancellation of Acoustic Scattering From a Sphere,” Physics Review Letters, 110, p. 124301 (2013).Google Scholar
16.Urzhumov, Y. A. and Smith, D. R., “Fluid Flow Control with Transformation Media,” Physics Review Letters, 107, p. 074501 (2011).Google Scholar
17.Fan, C., Gao, Y. and Huang, J., “Shaped Graded Materials with an Apparent Negative Thermal Conductivity,” Applied Physics Letters, 92, p. 251907 (2008).Google Scholar
18.Chen, T., Weng, C. N. and Chen, J. S., “Cloak for Curvilinearly Anisotropic Media in Conduction,” Applied Physics Letters, 93, p. 114103 (2008).Google Scholar
19.Zhang, S., Genov, D. A., Sun, C. and Zhang, X., “Cloaking if Matter Waves,” Physics Review Letters, 100, p. 123002 (2008).Google Scholar
20.Greenleaf, A., Kurylev, Y., Lassas, M., Leonhardt, U. and Uhlmann, G., “Cloaked Electromagnetic, Acoustic, and Quantum Amplifiers Via Transformation Optics,” Proceedings of the National Academy of Sciences of the United States of America, 109, pp. 10169–10174 (2012).Google Scholar
21.Narayana, S. and Sato, Y., “Heat Flux Manipulation with Engineered Thermal Materials,” Physics Review Letters, 108, p. 214303 (2012).Google Scholar
22.Cai, W. S., Chettiar, U. K., Kildishev, A. V. and Shalaev, V. M., “Optical Cloaking with Metamaterials,” Nature Photonics, 1, pp. 224–227 (2007).Google Scholar
23.Cai, W. S., Chettiar, U. K., Kildishev, A. V., Shalaev, V. M. and Milton, G. W., “Nonmagnetic Cloak with Minimized Scattering,” Applied Physics Letters, 91, p. 111105(2007).Google Scholar
24.Wood, B. and Pendry, J. B., “Metamaterials at Zero Frequency,” Journal of Physics: Condensed Matter, 19, p. 076208 (2007).Google Scholar
25.Wang, H. R., Xie, X., Hu, Y. T. and Wang, J., “Weakly Nonlinear Characteristics of a Three-Layer Circular Piezoelectric Plate-Like Power Harvester Near Resonance,” Journal of Mechanics, 30, pp. 97–102 (2014).Google Scholar
26.Ansari, R., Faghih Shojaei, M., Mohammadi, V., Gholami, R. and Rouhi, H., “Nonlinear Vibration Analysis of Microscale Functionally Graded Timo-shenko Beams Using the Most General Form of Strain Gradient Elasticity,” Journal of Mechanics, 30, pp. 161–172(2014).Google Scholar
27.Yan, M., Ruan, Z. and Qiu, M., “Scattering Characteristics of Simplified Cylindrical Invisibility Cloaks,” Optics Express, 15, p. 17772 (2007).Google Scholar
28.Chen, H. Y., Yang, T., Luo, X. D. and Ma, H. R., “Impedance-Matched Reduced Acoustic Cloaking with Realizable Mass and its Layered Density,” Chinese Physics Letters, 25, p. 3696 (2008).Google Scholar
29.Chen, H., Ng, J., Lee, C. W. J., Lai, Y. and Chan, C. T., “General Transformation for the Reduced Invisibility Cloak,” Physics Review B, 80, p. 085112 (2009).Google Scholar
30.Peng, L., Ran, L. and Mortensen, N. A., “The Scattering of a Cylindrical Invisibility Cloak: Reduced Parameters and Optimization,” Journal of Physics D: Applied Physics, 44, p. 135101 (2011).Google Scholar
31.Mittra, R. and Zhou, Y., “Application of Transformation Electromagnetics to Cloak Design and Reduction of Radar Cross Section,” Journal of Electromagnetic Engineering and Science, 13, pp. 73–85 (2013).Google Scholar
32.Chen, T. and Tsai, Y. L., “A Derivation for the Acoustic Material Parameters in Transformation Domains,” Journal of Sound and Vibration, 332, pp. 766–779 (2013).Google Scholar