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Dynamic Mass Density and Acoustic Metamaterials

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Acoustic Metamaterials and Phononic Crystals

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 173))

Abstract

Elastic and electromagnetic waves are two types of classical waves that, though very different, nevertheless display many analogous features. In particular, for the acoustic waves, there can be a correspondence between the two material parameters of the acoustic wave equation, the mass density and bulk modulus, with the dielectric constant and magnetic permeability of the Maxwell equations. We show that the classical mass density, a quantity that is often regarded as positive definite in value, can display complex finite-frequency characteristics for a composite that comprises local resonators, thereby leading to acoustic metamaterials in exact analogy with the electromagnetic metamaterials. In particular, we demonstrate that through the anti-resonance mechanism, a locally resonant sonic material is capable of totally reflecting low-frequency sound at a frequency where the effective dynamic mass density can approach positive and negative infinities. The condition that leads to the anti-resonance thereby offers a physical explanation of the metamaterial characteristics for both the membrane resonator and the 3D locally resonant sonic materials. Besides the metamaterials arising from the dynamic mass density behavior at finite frequencies, we also present a review of other relevant types of acoustic metamaterials. At the zero-frequency limit, i.e., in the absence of resonances, the dynamic mass density for the fluid–solid composites is shown to still differ significantly from the usual volume-averaged expression. We offer both a physical explanation and a rigorous mathematical derivation of the dynamic mass density in this case.

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References

  1. Z. Liu, X. Zhang, Y. Mao, Y.Y. Zhu, Z. Yang, C.T. Chan, P. Sheng, Locally resonant sonic materials. Science 289, 1734 (2000). It should be noted that in this initial publication the metamaterial characteristic was mis-attributed to negative elastic modulus. This was subsequently corrected in Ref. 2

    Google Scholar 

  2. Z. Liu, C. Chan, P. Sheng, Analytical model of phononic crystal with local resonances. Phys. Rev. B 71, 014103 (2005)

    Article  Google Scholar 

  3. P. Sheng, X. Zhang, Z. Liu, C. Chan, Locally resonant sonic materials. Physica B Condens. Matter 338, 201 (2003)

    Article  CAS  Google Scholar 

  4. J. Mei, Z. Liu, W. Wen, P. Sheng, Effective mass density of fluid-solid composites. Phys. Rev. Lett. 96, 24301 (2006)

    Article  Google Scholar 

  5. J. Mei, Z. Liu, W. Wen, P. Sheng, Effective dynamic mass density of composites. Phys. Rev. B 76, 134205 (2007)

    Article  Google Scholar 

  6. Y. Wu, Y. Lai, Z.Q. Zhang, Effective medium theory for elastic metamaterials in two dimensions. Phys. Rev. B 76, 205313 (2007)

    Article  Google Scholar 

  7. G.W. Milton, J.R. Willis, On modifications of Newton’s second law and linear continuum elastodynamics. Proc. R. Soc. A 463, 855 (2007)

    Article  Google Scholar 

  8. S. Yao, X. Zhou, G. Hu, Experimental study on negative effective mass in a 1d mass–spring system. New J. Phys. 10, 043020 (2008)

    Article  Google Scholar 

  9. D.L. Johnson, Equivalence between fourth sound in liquid He Ii at low temperatures and the Biot slow wave in consolidated porous media. Appl. Phys. Lett. 37, 1065 (1980)

    Article  CAS  Google Scholar 

  10. M.A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. J. Acoust. Soc. Am. 28, 168 (1956)

    Article  Google Scholar 

  11. T.J. Plona, Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies. Appl. Phys. Lett. 36, 259 (1980)

    Article  Google Scholar 

  12. P. Sheng, M.Y. Zhou, Dynamic permeability in porous media. Phys. Rev. Lett. 61, 1591 (1988)

    Article  Google Scholar 

  13. D. Weaire, Existence of a gap in the electronic density of states of a tetrahedrally bonded solid of arbitrary structure. Phys. Rev. Lett. 26, 1541 (1971)

    Article  CAS  Google Scholar 

  14. D.J. Ewins, Modal Testing: Theory, Practice and Application (Research Studies Press. Ltd., Hertfordshire, 2000)

    Google Scholar 

  15. M. Dilena, A. Morassi, The use of antiresonances for crack detection in beams. J. Sound Vib. 276, 195 (2004)

    Article  Google Scholar 

  16. M. Dilena, A. Morassi, Damage detection in discrete vibrating systems. J. Sound Vib. 289, 830 (2006)

    Article  Google Scholar 

  17. G. Schitter, K.J. Astrom, B.E. DeMartini, P.J. Thurner, K.L. Turner, P.K. Hansma, Design and modeling of a high-speed Afm-scanner. IEEE Trans. Control. Syst. Technol. 15, 906 (2007)

    Article  Google Scholar 

  18. G. Schitter, F. Allgöwer, A. Stemmer, A new control strategy for high-speed atomic force microscopy. Nanotechnology 15, 108 (2004)

    Article  CAS  Google Scholar 

  19. G. Schitter, P.J. Thurner, P.K. Hansma, Design and input-shaping control of a novel scanner for high-speed atomic force microscopy. Mechatronics 18, 282 (2008)

    Article  Google Scholar 

  20. Z. Yang, J. Mei, M. Yang, N. Chan, P. Sheng, Membrane-type acoustic metamaterial with negative dynamic mass. Phys. Rev. Lett. 101, 204301 (2008)

    Article  CAS  Google Scholar 

  21. S.H. Lee, C.M. Park, Y.M. Seo, Z.G. Wang, C.K. Kim, Acoustic metamaterial with negative density. Phys. Lett. A 373, 4464 (2009)

    Article  CAS  Google Scholar 

  22. S. Yao, X. Zhou, G. Hu, Investigation of the negative-mass behaviors occurring below a cut-off frequency. New J. Phys. 12, 103025 (2010)

    Article  Google Scholar 

  23. Z. Yang, H. Dai, N. Chan, G. Ma, P. Sheng, Acoustic metamaterial panels for sound attenuation in the 50–1000 Hz regime. Appl. Phys. Lett. 96, 041906 (2010)

    Article  Google Scholar 

  24. L. Landau, E. Lifshitz, Theory of Elasticity, 3rd edn. (Elmsford, New York, 1982)

    Google Scholar 

  25. J. Li, C. Chan, Double-negative acoustic metamaterial. Phys. Rev. E 70, 055602 (2004)

    Article  Google Scholar 

  26. Y. Ding, Z. Liu, C. Qiu, J. Shi, Metamaterial with simultaneously negative bulk modulus and mass density. Phys. Rev. Lett. 99, 93904 (2007)

    Article  Google Scholar 

  27. N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, X. Zhang, Ultrasonic metamaterials with negative modulus. Nat. Mater. 5, 452 (2006)

    Article  CAS  Google Scholar 

  28. L. Fok, M. Ambati, X. Zhang, Acoustic metamaterials. MRS Bull. 33, 931 (2008)

    Article  CAS  Google Scholar 

  29. C. Ding, L. Hao, X. Zhao, Two-dimensional acoustic metamaterial with negative modulus. J. Appl. Phys. 108, 074911 (2010)

    Article  Google Scholar 

  30. C.L. Ding, X.P. Zhao, Multi-band and broadband acoustic metamaterial with resonant structures. J. Phys. D Appl. Phys. 44, 215402 (2011)

    Article  Google Scholar 

  31. S.H. Lee, C.M. Park, Y.M. Seo, Z.G. Wang, C.K. Kim, Acoustic metamaterial with negative modulus. J. Phys. Condens. Matter 21, 175704 (2009)

    Article  Google Scholar 

  32. C. Goffaux, J. Sánchez-Dehesa, A.L. Yeyati, P. Lambin, A. Khelif, J. Vasseur, B. Djafari-Rouhani, Evidence of fano-like interference phenomena in locally resonant materials. Phys. Rev. Lett. 88, 225502 (2002)

    Article  CAS  Google Scholar 

  33. Y. Cheng, J. Xu, X. Liu, One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus. Phys. Rev. B 77, 045134 (2008)

    Article  Google Scholar 

  34. X. Hu, K.M. Ho, C. Chan, J. Zi, Homogenization of acoustic metamaterials of Helmholtz resonators in fluid. Phys. Rev. B 77, 172301 (2008)

    Article  Google Scholar 

  35. S.H. Lee, C.M. Park, Y.M. Seo, Z.G. Wang, C.K. Kim, Composite acoustic medium with simultaneously negative density and modulus. Phys. Rev. Lett. 104, 54301 (2010)

    Article  Google Scholar 

  36. S.H. Lee, C.M. Park, Y.M. Seo, C.K. Kim, Reversed Doppler effect in double negative metamaterials. Phys. Rev. B 81, 241102 (2010)

    Article  Google Scholar 

  37. M. Ambati, N. Fang, C. Sun, X. Zhang, Surface resonant states and superlensing in acoustic metamaterials. Phys. Rev. B 75, 195447 (2007)

    Article  Google Scholar 

  38. S. Guenneau, A. Movchan, G. PĂ©tursson, S. Anantha Ramakrishna, Acoustic metamaterials for sound focusing and confinement. New J. Phys. 9, 399 (2007)

    Article  Google Scholar 

  39. K. Deng, Y. Ding, Z. He, H. Zhao, J. Shi, Z. Liu, Theoretical study of subwavelength imaging by acoustic metamaterial slabs. J. Appl. Phys. 105, 124909 (2009)

    Article  Google Scholar 

  40. X. Zhou, G. Hu, Superlensing effect of an anisotropic metamaterial slab with near-zero dynamic mass. Appl. Phys. Lett. 98, 263510 (2011)

    Article  Google Scholar 

  41. J. Li, Z. Liu, C. Qiu, Negative refraction imaging of acoustic waves by a two-dimensional three-component phononic crystal. Phys. Rev. B 73, 054302 (2006)

    Article  Google Scholar 

  42. S. Zhang, L. Yin, N. Fang, Focusing ultrasound with an acoustic metamaterial network. Phys. Rev. Lett. 102, 194301 (2009)

    Article  Google Scholar 

  43. L. Zigoneanu, B.I. Popa, S.A. Cummer, Design and measurements of a broadband two-dimensional acoustic lens. Phys. Rev. B 84, 024305 (2011)

    Article  Google Scholar 

  44. P.A. Belov, C.R. Simovski, P. Ikonen, Canalization of subwavelength images by electromagnetic crystals. Phys. Rev. B 71, 193105 (2005)

    Article  Google Scholar 

  45. Y. Jin, S. He, Canalization for subwavelength focusing by a slab of dielectric photonic crystal. Phys. Rev. B 75, 195126 (2007)

    Article  Google Scholar 

  46. Z. He, F. Cai, Y. Ding, Z. Liu, Subwavelength imaging of acoustic waves by a canalization mechanism in a two-dimensional phononic crystal. Appl. Phys. Lett. 93, 233503 (2008)

    Article  Google Scholar 

  47. X. Ao, C. Chan, Far-field image magnification for acoustic waves using anisotropic acoustic metamaterials. Phys. Rev. E 77, 025601 (2008)

    Article  Google Scholar 

  48. Z. Jacob, L.V. Alekseyev, E. Narimanov, Optical hyperlens: far-field imaging beyond the diffraction limit. Opt. Express 14, 8247 (2006)

    Article  Google Scholar 

  49. Z. Liu, H. Lee, Y. Xiong, C. Sun, X. Zhang, Far-field optical hyperlens magnifying sub-diffraction-limited objects. Science 315, 1686 (2007)

    Article  CAS  Google Scholar 

  50. D. Smith, D. Schurig, Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors. Phys. Rev. Lett. 90, 77405 (2003)

    Article  CAS  Google Scholar 

  51. J. Li, L. Fok, X. Yin, G. Bartal, X. Zhang, Experimental demonstration of an acoustic magnifying hyperlens. Nat. Mater. 8, 931 (2009)

    Article  CAS  Google Scholar 

  52. F. Liu, F. Cai, S. Peng, R. Hao, M. Ke, Z. Liu, Parallel acoustic near-field microscope: a steel slab with a periodic array of slits. Phys. Rev. E 80, 026603 (2009)

    Article  Google Scholar 

  53. J. Zhu, J. Christensen, J. Jung, L. Martin-Moreno, X. Yin, L. Fok, X. Zhang, F. Garcia-Vidal, A holey-structured metamaterial for acoustic deep-subwavelength imaging. Nat. Phys. 7, 52 (2010)

    Article  CAS  Google Scholar 

  54. A. Spadoni, C. Daraio, Generation and control of sound bullets with a nonlinear acoustic lens. Proc. Natl. Acad. Sci. 107, 7230 (2010)

    Article  CAS  Google Scholar 

  55. G.W. Milton, M. Briane, J.R. Willis, On cloaking for elasticity and physical equations with a transformation invariant form. New J. Phys. 8, 248 (2006)

    Article  Google Scholar 

  56. H. Chen, C. Chan, Acoustic cloaking in three dimensions using acoustic metamaterials. Appl. Phys. Lett. 91, 183518 (2007)

    Article  Google Scholar 

  57. S.A. Cummer, D. Schurig, One path to acoustic cloaking. New J. Phys. 9, 45 (2007)

    Article  Google Scholar 

  58. Y. Cheng, F. Yang, J.Y. Xu, X.J. Liu, A multilayer structured acoustic cloak with homogeneous isotropic materials. Appl. Phys. Lett. 92, 151913 (2008)

    Article  Google Scholar 

  59. J. Pendry, J. Li, An acoustic metafluid: realizing a broadband acoustic cloak. New J. Phys. 10, 115032 (2008)

    Article  Google Scholar 

  60. D. Torrent, J. Sánchez-Dehesa, Acoustic cloaking in two dimensions: a feasible approach. New J. Phys. 10, 063015 (2008)

    Article  Google Scholar 

  61. S.A. Cummer, B.I. Popa, D. Schurig, D.R. Smith, J. Pendry, M. Rahm, A. Starr, Scattering theory derivation of a 3d acoustic cloaking shell. Phys. Rev. Lett. 100, 24301 (2008)

    Article  Google Scholar 

  62. A.N. Norris, Acoustic cloaking theory. Proc. R. Soc. A 464, 2411 (2008)

    Article  CAS  Google Scholar 

  63. Y. Urzhumov, F. Ghezzo, J. Hunt, D.R. Smith, Acoustic cloaking transformations from attainable material properties. New J. Phys. 12, 073014 (2010)

    Article  Google Scholar 

  64. Y. Bobrovnitskii, Impedance acoustic cloaking. New J. Phys. 12, 043049 (2010)

    Article  Google Scholar 

  65. Z. Liang, J. Li, Bending a periodically layered structure for transformation acoustics. Appl. Phys. Lett. 98, 241914 (2011)

    Article  Google Scholar 

  66. X. Zhu, B. Liang, W. Kan, X. Zou, J. Cheng, Acoustic cloaking by a superlens with single-negative materials. Phys. Rev. Lett. 106, 14301 (2011)

    Article  Google Scholar 

  67. H. Chen, C. Chan, Acoustic cloaking and transformation acoustics. J. Phys. D Appl. Phys. 43, 113001 (2010)

    Article  Google Scholar 

  68. M. Farhat, S. Enoch, S. Guenneau, A. Movchan, Broadband cylindrical acoustic cloak for linear surface waves in a fluid. Phys. Rev. Lett. 101, 134501 (2008)

    Article  CAS  Google Scholar 

  69. M. Farhat, S. Guenneau, S. Enoch, A.B.. Movchan, Cloaking bending waves propagating in thin elastic plates. Phys. Rev. B 79, 033102 (2009)

    Article  Google Scholar 

  70. M. Farhat, S. Guenneau, S. Enoch, Ultrabroadband elastic cloaking in thin plates. Phys. Rev. Lett. 103, 24301 (2009)

    Article  Google Scholar 

  71. A. Norris, A. Shuvalov, Elastic cloaking theory. Wave Motion 48, 525–538 (2011)

    Article  Google Scholar 

  72. Y.A. Urzhumov, D.R. Smith, Fluid flow control with transformation media. Phys. Rev. Lett. 107, 074501 (2011)

    Article  Google Scholar 

  73. S. Zhang, C. Xia, N. Fang, Broadband acoustic cloak for ultrasound waves. Phys. Rev. Lett. 106, 24301 (2011)

    Article  Google Scholar 

  74. B.I. Popa, L. Zigoneanu, S.A. Cummer, Experimental acoustic ground cloak in air. Phys. Rev. Lett. 106, 253901 (2011)

    Article  Google Scholar 

  75. B. Liang, B. Yuan, J. Cheng, Acoustic diode: rectification of acoustic energy flux in one-dimensional systems. Phys. Rev. Lett. 103, 104301 (2009)

    Article  Google Scholar 

  76. B. Liang, X. Guo, J. Tu, D. Zhang, J. Cheng, An acoustic rectifier. Nat. Mater. 9, 989 (2010)

    Article  CAS  Google Scholar 

  77. N. Boechler, G. Theocharis, C. Daraio, Bifurcation-based acoustic switching and rectification. Nat. Mater. 10, 665 (2011)

    Article  CAS  Google Scholar 

  78. X.F. Li, X. Ni, L. Feng, M.H. Lu, C. He, Y.F. Chen, Tunable unidirectional sound propagation through a sonic-crystal-based acoustic diode. Phys. Rev. Lett. 106, 84301 (2011)

    Article  Google Scholar 

  79. Y. Lai, Y. Wu, P. Sheng, Z.Q. Zhang. Hybrid elastic solids. Nat. Mater. 10, 620 (2011)

    Google Scholar 

  80. J. Mei, Z. Liu, J. Shi, D. Tian, Theory for elastic wave scattering by a two-dimensional periodical array of cylinders: an ideal approach for band-structure calculations. Phys. Rev. B 67, 245107 (2003)

    Article  Google Scholar 

  81. J. Mei, Z. Liu, C. Qiu, Multiple-scattering theory for out-of-plane propagation of elastic waves in two-dimensional phononic crystals. J. Phys. Condens. Matter 17, 3735 (2005)

    Article  CAS  Google Scholar 

  82. P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, vol. 88, Springer Series in Materials Science (Springer, 2006)

    Google Scholar 

  83. J.G. Berryman, Long wavelength propagation in composite elastic media I. Spherical inclusions. J. Acoust. Soc. Am. 68, 1809 (1980)

    Article  Google Scholar 

  84. L.M. Schwartz, D.L. Johnson, Long-wavelength acoustic propagation in ordered and disordered suspensions. Phys. Rev. B 30, 4302 (1984)

    Article  Google Scholar 

  85. R. Lakes, T. Lee, A. Bersie, Y. Wang, Extreme damping in composite materials with negative-stiffness inclusions. Nature 410, 565 (2001)

    Article  CAS  Google Scholar 

  86. F. Cervera, L. Sanchis, J. Sanchez-Perez, R. Martinez-Sala, C. Rubio, F. Meseguer, C. Lopez, D. Caballero, J. Sanchez-Dehesa, Refractive acoustic devices for airborne sound. Phys. Rev. Lett. 88, 23902 (2001)

    Article  Google Scholar 

  87. J. Mei, Y. Wu, Z. Liu, Effective medium of periodic fluid-solid composites, Eur. Phys. Lett. 98, 54001 (2012)

    Google Scholar 

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Acknowledgments

Research works in dynamic mass density and membrane-type acoustic metamaterials have been supported by Hong Kong Research Grant Council grants HKUST6145/99P, HKUST6143/00P, HKUST 605405, and HKUST604207.

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Authors and Affiliations

  1. Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

    Jun Mei, Guancong Ma, Min Yang, Jason Yang & Ping Sheng

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  1. Jun Mei
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  2. Guancong Ma
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Correspondence to Ping Sheng .

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  1. , Dept. of Materials Science and Engineeri, University of Arizona, East James E. Rogers Way 1235, Tucson, 85721-0012, Arizona, USA

    Pierre A. Deymier

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Mei, J., Ma, G., Yang, M., Yang, J., Sheng, P. (2013). Dynamic Mass Density and Acoustic Metamaterials. In: Deymier, P. (eds) Acoustic Metamaterials and Phononic Crystals. Springer Series in Solid-State Sciences, vol 173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31232-8_5

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  • DOI: https://doi.org/10.1007/978-3-642-31232-8_5

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