屏蔽裝置近年來發展在各個領域中，從電磁波到光學、聲學、熱傳學及彈性波，Pendry et al. (2006)及Leonhardt (2006)提出在電磁波理論中利用座標轉換的概念實現屏蔽效應，但屏蔽材料在實際製造較為困難，須使用超材料來達成。本文探討反平面剪力(SH)波的屏蔽裝置，提出一階材料簡化與高階座標轉換的手法，其中一階材料簡化為藉由滿足慢度曲線(slowness curve)公式進行簡化，使得材料參數變為僅剩一個變數，而高階座標轉換手法為透過質量密度假設為定值反推高階座標轉換公式，可簡化材料僅剩二個變數。將上述二種方式應用在層狀屏蔽裝置，透過數值模擬在不同波長下的屏蔽效果。本文提出一個以2種等向性材料透過面積上的配比方法設計出20層的屏蔽裝置，因為現實中此2種材料容易取得，故增加此屏蔽裝置在實際製造上可行性。

Recently, rapid progress has been made in controlling the wave propagation with meta-devices, such as Pendry et al. (2006) and Leonhardt (2006) who used coordinate transformation method to design an electromagnetic cloak. However, the experimental realization of these cloaks demand complex material parameters, which are not easy to fabricate. For this reason, we propose a design for a multilayered cloak that can manipulate the propagation of an antiplane shear wave. We multiply the parameters for an ideal cloak by using an arbitrary function; thus, the spatially varying parameters can be reduced from three to one while the slowness curve remains unchanged. We also demonstrate how to find the specific transformation which makes the density become homogeneous for a transformation device. For numerical illustration, our design shows good performance compared to reported references. Finally, we present a cloak that consists of 20 layers of alternating concentric layers. Such cloak is more feasible to manufacture since only two kinds of isotropic materials are required.

Auld, B. A. Acoustic fields and waves in solids. Рипол Классик (1973).

Brun, M., Guenneau S. and Movchan, A., Achieving control of in-plane elastic waves, Applied Physics Letters 94, 061903 (2009).

Brun, M., Colquitt, D. J., Jones, I. S., Movchan, A. B., & Movchan, N. V. Transformation cloaking and radial approximations for flexural waves in elastic plates. New Journal of Physics 16(9), 093020 (2014).

Cai, L.-W. and Sánchez-Dehesa, J., Analysis of Cummer-Schurig acoustic cloaking, New Journal of Physics 9, 450 (2007).

Chen, H. and Chan, C. T., Acoustic cloaking in three dimensions using acoustic metamaterials, Applied Physics Letters 91(18), 183518 (2007).

Chen, H. and Chan, C. T., Electromagnetic wave manipulation by latered systems using the transformation media concept, Physical Review B, 78(5), 054204 (2008).

Chen, H., Ng, J., Lee, C. J., Lai, Y., & Chan, C. T. General transformation for the reduced invisibility cloak. Physical Review B 80(8), 085112 (2009).

Chen, T. and Weng, C. N., Invisibility cloak with a twin cavity, Optics express 17(10), 8614-8620 (2009).

Chen, T. and Tsai, Y. L., A derivation for the acoustic material parameters in transformation domains, Journal of Sound and Vibration 332, 766-779 (2013)

Cummer, S. A., Popa, B.-I., Schurig, D. and Smith, D. R., Full-wave simulations of electromagnetic cloaking structures, Physical Review E 74, 036621 (2006).

Cummer, S.A., and Schurig, D., One path to acoustic cloaking, New Journal of Physics 9, 45 (2007).

Farhat, M., Guenneau, S., Enoch, S. and Movchan, A., Cloaking bending waves propagating in thin elastic plates, Physical Review B 79, 033102 (2009a).

Farhat, M., Guenneau, S., Enoch, S. Ultrabroadband elastic cloaking in thin plates, Physical review letters 103(2), 024301 (2009b).

Graff, K. F. Wave motion in elastic solids. Courier Corporation. (1968).

Guenneau, S., Amra, C., and Veynante, D., Transformation thermodynamics:cloaking and concentrating heat flux, Optics Express 20(7), 8207-8218 (2012).

Huang, Y., Feng, Y. and Jiang, T., Electromagnetic cloaking by layered structure of homogeneous isotropic materials, Optics Express 15, 11133 (2007).

Han, T., Yuan, T., Li, B. and Qiu, C.-W., Homogeneous Thermal Cloak with Constant Conductivity and Tunable Heat Localization, Scientific Reports 10, 1593 (2013).

Jiang, W. X. and Cui, T. J., Moving targets virtually via composite optical transformation, Optics Express 18(5), 5651 (2010).

Khlopotin, A., & Razanica, S. Designing Materials for Mechanical Invisibility Cloaks (2012).

Leissa, A. W. Vibration of plates. Ohio state univ columbus (1969).

Lai, Y., Chen, H., Zhang, Z. Q. and Chan, C. T., Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell, Physical Review Letters 102(9), 093901 (2009a).

Lai, Y., Ng, J., Chen, H., Han, D., Xiao, J., Zhang, Z. Q. and Chan, C. T., Illusion optics: The optical transformation of an object into another object, Physical Review Letters 102(25), 253902 (2009b).

Leonhardt, U., Optical conformal mapping, Science 312 (5781), 1777 (2006).

Leonhardt, U., Cloak of heat, Nature 498, 440-441 (2013).

Luo, Y., Chen, H., Zhang, J., Ran, L. and Kong, J. A., Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations, Physical Review B 77(12), 125127 (2008).

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, 248 (2006).

Milton, G. W., and Willis, J. R., On modifications of Newton's second law and linear continuum elastodynamics, Proceedings of the Royal Society A 463 2079 (2007).

Ma, H., Qu, S., Xu, Z. and Wang, J., Approximation approach of designing practical cloaks with arbitrary shapes, Optics Express 16(20), 15449-15454 (2008).

Nayfeh, A. H., Wave propagation in layered anisotropic media: With application to composites. Elsevier.Xiang (1995).

Norris, A. N. And Shnvalov, A. L., Elastic cloaking theory, Wave Motion 48, 525 (2011).

Norris, A. N., and Parnell, W. J., Hyperelastic cloaking theory: transformation elasticity with pre-stressed solids., Proceedings of the Royal Society A, 468, 2146, (2012) .

Pendry, J. B., Schurig, D. and Smith, D. R., Controlling electromagnetic fields, Science 312, 1780 (2006).

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 transfromations of Maxwell’s equations, Photonics and Nanostructures – Fundamentals and Applications 6, 87 (2008).

Stenger, N., Wilhelm, M. and Wegener, M., Experiments on elastic cloaking in thin plates, Physical Review Letters 108, 014301 (2012).

Tichit, P. H., Kanté, B., Burokur, S. N. and Lustrac, A., Design of polygonal and elliptical invisibility cloaks, Institut d’Electronique Fondamentale, CNRS UMR 8622-Universit Paris Sud 11-91405 Orsay-France (2008).

Tsai, Y. L. and Chen, T., Tailoring Specific Heat and Density in the Design of Thermal Transformation Media, Session 2P5a SC2: Thermal and Acoustic Metamaterials 788, (2014).

Veselago, V. G., The electrodynamics of substances with simultaneously negative values of  and , Soviet Physics Uspekhi 10, 509 (1975).

Wu, Q., Zhang, K., Meng, F. and Li, L., Material parameters characterization for arbitrary N-sided regular polygonal invisible cloak, Journal of Physics D Applied Physics 42, 035408 (2009).

Xiang, Z. The form-invariance of wave equations without requiring a priori relations between field variables. Science China Physics, Mechanics & Astronomy 57(12), 2285-2296. (2014).

You, Y., Kattawar, G. W., Zhai, P. W. and Yang, P., Invisibility cloaks for irregular particles using coordinate transformations, Optics Express 16, 6134-6145 (2008).

Yan, M., Ruan, Z. and Qiu, M., Scattering characteristics of simplified cylindrical invisibility cloaks, Optics Express 16 (9), 6134 (2007).

Yang, T, Chen, H. Y., Luo, X. D. and Ma, H. R., Superscatterer: Enhancement of scattering with complementary media, Optics Express 16 (22), 18545 (2008).

Yang, T., Huang, L., Chen, F. and Xu, W., Heat flux and temperature field cloaks for arbitrarily shaped objects, Journal of Physics D Applied Physics 46, 305102 (2013).

Zhang, J., Luo, Y., Chen, H. and Wu, B. I., Cloak of arbitrary shape, Journal of the Optical Society of America B 25, 1776-1779 (2008).

蔡育霖，電磁波在不同形狀轉換材料的模擬，國立成功大學土木所碩士論文 (2009).

翁崇寧，轉換材料在不同物理與彈性問題之理論及等效行為探討，國立成功大學博士論文 (2010).

鍾文曉，層狀聲學斗篷之材料與幾何最佳化設計，國立成功大學碩士論文 (2012).

張晉銓，利用座標轉換法來模擬熱流傳播方向的控制，國立成功大學碩士論文 (2014).