Frontiers of Mechanical Engineering >
Analytical solution for SH wave propagating through a graded plate of metamaterial
Received date: 02 Mar 2011
Accepted date: 20 Jul 2011
Published date: 05 Sep 2011
Copyright
A physical model for the shear horizontal (SH) wave propagating from left-handed material (LHM) through a graded or transition layer to right-handed material (RHM) has been proposed in this paper. After the comparison of the basic wave equations of the electromagnetic, longitudinal, and SH waves, it is found that they take similar differential form. The analytical solutions have been found for power law, hyperbolic, and polynomial profiles. Numerical waveforms of the amplitude and phase of the displacement are obtained for the corresponding profiles. It is found that the waveforms are symmetric for the power law and hyperbolic profiles, and that the waveform for the polynomial profile is shifted and non-symmetric. The shift along with the anti-symmetric profile may provide a way to monitor the wave behavior of the metamaterials.
Jinfeng ZHAO , Yongdong PAN , Zheng ZHONG . Analytical solution for SH wave propagating through a graded plate of metamaterial[J]. Frontiers of Mechanical Engineering, 2011 , 6(3) : 301 -307 . DOI: 10.1007/s11465-011-0238-7
| 1 |
Veselago V G. The electrodynamics of substances with simultaneously negative values of ϵ and μ. Soviet Physics USPEKI, 1968, 10(4): 509–514
|
| 2 |
Shelby R A, Smith D R, Schultz S. Experimental verification of a negative index of refraction. Science, 2001, 292(5514): 77–79
|
| 3 |
Li J, Chan C T. Double-negative acoustic metamaterial. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2004, 70(5): 055602–055605
|
| 4 |
Chan C T, Li J, Fung K H. On extending the concept of double negativity to acoustic waves. Journal of Zhejiang University Science A, 2006, 7(1): 24–28
|
| 5 |
Zhou X M, Hu G K. Analytic model of elastic metamaterials with local resonances. Physical Review B: Condensed Matter and Materials Physics, 2009, 79(19): 195109–195117
|
| 6 |
Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K. Composite acoustic medium with simultaneously negative density and modulus. Physical Review Letters, 2010, 104(5): 054301–054304
|
| 7 |
Smith D R, Mock J J, Starr A F, Schurig D. Gradient index metamaterials. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2005, 71(3): 036609–036614
|
| 8 |
Dalarsson M, Tassin P. Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material. Optics Express, 2009, 17(8): 6747–6752
|
| 9 |
Ingrey P C, Hopcraft K I, Jakeman E, French O E. Between right- and left-handed media. Optics Communications, 2009, 282(5): 1020–1027
|
| 10 |
Kong J A. Electromagnetic Wave Theory. Beijing: Higher Education Press, 2002, 122–124(in Chinese)
|
| 11 |
Cummer S A, Popa B I, Schurig D, Smith D R, Pendry J, Rahm M, Starr A. Scattering theory derivation of a 3D acoustic cloaking shell. Physical Review Letters, 2008, 100(2): 024301–024304
|
| 12 |
Milton G W, Briane M, Willis J R. On cloaking for elasticity and physical equations with a transformation invariant form. New Journal of Physics, 2006, 8(10): 248–267
|
| 13 |
Zhang L G, Gai B Z, Zhu H. SH-wave propagation in functionally graded materials. Journal of Harbin University of Commerce (Natural Sciences Edition), 2007, 23(1): 80–85
|
| 14 |
Schurig D, Mock J J, Justice B J, Cummer S A, Pendry J B, Starr A F, Smith D R. Metamaterial electromagnetic cloak at microwave frequencies. Science, 2006, 314(5801): 977–980
|
| 15 |
Zhang S, Xia C G, Fang N. Broadband acoustic cloak for ultrasound waves. Physical Review Letters, 2011, 106(2): 024301–024312
|
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