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In this paper, we present a metamaterial beam consisting of a uniform isotropic beam with many small mass-spring systems serving as mechanical wave absorbers. Based on the analysis of two different mass-spring systems, negative effective mass and negative effective stiffness are explained theoretically. The governing equations of a unit cell of a metamaterial beam are derived using the Hamilton’s principle. The mechanical wave absorbabilities of the following two different finite metamaterial beams are analyzed by numerical simulation:one is the bean in which mass-spring systems with linearly varying elastic coefficients are uniformly distributed, and the other is the bean in which four identical absorber subgroups composed of spring-damper subsystems with linearly varying natural frequenciesare uniformly distributed. The results reveal that the mechanical wave transmitted in the metamaterial beam is absorbed by resonating with spring-mass absorbers, which verifies the effectivity of the proposed metamaterial beam on mechanical wave absorption.
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Keywords:
- metamaterial beam /
- negative effective mass /
- negative effective stiffness /
- mechanical wave
[1] Sachan M, Majetich S 2005 DARPA Meta-Materials Program Report
[2] Liu S 2005 DARPA Meta-Materials Program Report
[3] Chen C 2005 DARPA Meta-Materials Program Report
[4] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[5] Li J, Chan C T 2004 Phys. Rev. E 70 0225602
[6] Wu Y, Lai Y, Zhang 2007 Phys. Rev. B 76 205313
[7] Milton G W, Willis J R 2007 Proc. R. Soc. A 463 855
[8] Cheng Y, Xu J Y, Liu X J 2008 Phys. Rev. B 77 045134
[9] Huang, H H, Sun, C T, Huang, G L 2009 Int. J. of Engineering Science 47 610
[10] Fang N, Xi D J, Xu J Y, Ambati M, Srituravanich W, Sun C, Zhang X 2006 Nature Mater. 5 452
[11] Ding C L, Zhao X P 2009 Acta Phys. Sin. 58 6351(in Chinese) [丁昌林、赵晓鹏 2009 物理学报 58 6351]
[12] Akl W, Baz A 2010 J. Intell. Mater. Syst. Struct. 12 541
[13] Sheng P, Zhang X X, Liu Z, Chan C T 2003 Physica B 338 201
[14] Hirsekorn M, Delsanto P P, Batra N K, Matic P 2004 Ultrasonics 42 231
[15] Yao S S, Zhou X M, Hu G K 2008 New J. Phys. 100 043020
[16] Huang H H, Sun C T, Huang G L 2009 Int. J. Eeg. Sci. 47 610
[17] Huang H H, Sun C T 2009 New J. Phys. 11 013003
[18] Cheng Y, Xu J Y, Liu X J 2008 Phys. Rev. B 77 045134
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[1] Sachan M, Majetich S 2005 DARPA Meta-Materials Program Report
[2] Liu S 2005 DARPA Meta-Materials Program Report
[3] Chen C 2005 DARPA Meta-Materials Program Report
[4] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[5] Li J, Chan C T 2004 Phys. Rev. E 70 0225602
[6] Wu Y, Lai Y, Zhang 2007 Phys. Rev. B 76 205313
[7] Milton G W, Willis J R 2007 Proc. R. Soc. A 463 855
[8] Cheng Y, Xu J Y, Liu X J 2008 Phys. Rev. B 77 045134
[9] Huang, H H, Sun, C T, Huang, G L 2009 Int. J. of Engineering Science 47 610
[10] Fang N, Xi D J, Xu J Y, Ambati M, Srituravanich W, Sun C, Zhang X 2006 Nature Mater. 5 452
[11] Ding C L, Zhao X P 2009 Acta Phys. Sin. 58 6351(in Chinese) [丁昌林、赵晓鹏 2009 物理学报 58 6351]
[12] Akl W, Baz A 2010 J. Intell. Mater. Syst. Struct. 12 541
[13] Sheng P, Zhang X X, Liu Z, Chan C T 2003 Physica B 338 201
[14] Hirsekorn M, Delsanto P P, Batra N K, Matic P 2004 Ultrasonics 42 231
[15] Yao S S, Zhou X M, Hu G K 2008 New J. Phys. 100 043020
[16] Huang H H, Sun C T, Huang G L 2009 Int. J. Eeg. Sci. 47 610
[17] Huang H H, Sun C T 2009 New J. Phys. 11 013003
[18] Cheng Y, Xu J Y, Liu X J 2008 Phys. Rev. B 77 045134
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