RSS feeds
РусскийEnglish
Issue 12, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2011

 / 

June

←  →

Reviews of topical problems


Acoustic gradient barriers (exactly solvable models)

 a, b,  b
a Joint Institute for High Temperatures, Russian Academy of Sciences, ul. Izhorskaya 13/19, Moscow, 127412, Russian Federation
b Space Research Institute, Russian Academy of Sciences, Profsoyuznaya str. 84/32, Moscow, 117997, Russian Federation

This paper reviews the physical fundamentals and mathematical formalism for problems concerning acoustic waves passing through gradient wave barriers formed by a continuous one-dimensional spatial distribution of the density and/or elastic parameters of a medium in a finite-thickness layer. The physical mechanisms of such processes involve nonlocal (geometric) normal and anomalous dispersion determined by the profiles and geometric parameters of the gradient barrier. The relevant mathematics relies on exactly solvable gradient barrier models with up to three free parameters and on the auxiliary barrier method with which the exactly solvable models found can be used to build new, also exactly solvable, models for such barriers. The longitudinal and shear wave transmission spectra through the gradient barriers considered are presented, and the dependence of these spectra on the gradient and curvature of the density distribution and on the elastic parameters of the barrier is expressed using general formulas corresponding to the geometrical and abnormal geometric dispersion. Examples of reflectionless tunneling of sound through gradient barriers formed either by the elastic parameter distribution in an inhomogeneous layer or by curvilinear boundaries of a homogeneous layer are considered. It is also shown that by using subwavelength gradient barriers and periodic structures composed of them, phonon crystal elements can be fabricated.

Fulltext pdf (378 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0181.201106c.0627
PACS: 43.60.Vx, 51.40.+p, 62.60.+v, 68.35.Iv (all)
DOI: 10.3367/UFNe.0181.201106c.0627
URL: https://ufn.ru/en/articles/2011/6/c/
000296147800003
2-s2.0-80052788744
2011PhyU...54..605S
Citation: Shvartsburg A B, Erokhin N S "Acoustic gradient barriers (exactly solvable models)" Phys. Usp. 54 605–623 (2011)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 8th, September 2010, revised: 20th, November 2010, 12th, January 2011

Оригинал: Шварцбург А Б, Ерохин Н С «Градиентные акустические барьеры (точно решаемые модели)» УФН 181 627–646 (2011); DOI: 10.3367/UFNr.0181.201106c.0627

References (54) ↓ Cited by (6) Similar articles (20)

  1. Slawinski M A Seismic Waves And Rays In Elastic Media (Amsterdam: Pergamon, 2003)
  2. Zaman F D, Al-Muhiameed Z I A Appl. Acoust. 61 427 (2000)
  3. Taroyan V, Erdélyi R Proc. Int. Astron. Union 3 86 (2007)
  4. Sheng P et al. Physica B 338 201 (2003)
  5. Milton G W, Briane M, Willis J R New J. Phys. 8 248 (2006)
  6. Chen H, Chan C T Appl. Phys. Lett. 91 183518 (2007)
  7. Lee S-J et al. Appl. Phys. Lett. 82 2133 (2003)
  8. Ben-Amoz M Z. Angew. Math. Phys. 27 83 (1976)
  9. Chakraborty A J. Acoust. Soc. Am. 123 56 (2008)
  10. Shvartsburg A B, Kuzmiak V, Petite G Phys. Rep. 452 33 (2007)
  11. Landau L D, Lifshits E M Teoriya Uprugosti (M.: Nauka, 1987); Landau L D, Lifshitz E M Theory Of Elasticity (Oxford: Pergamon Press, 1986)
  12. Mindlin R D Int. J. Solids Struct. 1 417 (1965)
  13. Erofeyev V I Wave Processes In Solids With Microstructure (River Edge, NJ: World Scientific, 2003)
  14. Bennett T, Gitman I M, Askes H Int. J. Fract. 148 185 (2007)
  15. Vavva M G et al. J. Acoust. Soc. Am. 125 3414 (2009)
  16. Kravtsov Yu A Akust. Zhurn. 14 1 (1968); Kravtsov Yu A Sov. Phys. Acoust. 14 1 (1968)
  17. Brekhovskikh L M, Godin O A Akustika Sloistykh Sred (M.: Nauka, 1989); Brekhovskikh L M, Godin O A Acoustics Of Layered Media, I, II (Berlin: Springer-Verlag, 1990, 1992)
  18. Strutt J W (Baron Rayleigh) The Theory Of Sounds (London: Macmillan and Co., 1937); Strett D V (lord Relei) Teoriya Zvuka (M.: GITTL, 1940)
  19. Godin O A, Chapman D M F J. Acoust. Soc. Am. 106 2367 (1999)
  20. Miropol’skii Yu Z Dinamika Vnutrennikh Gravitatsionnykh Voln v Okeane (L.: Gidrometeoizdat, 1981)
  21. Talipova T G, Pelinovskii E N, Petrukhin N S Okeanologiya 49 673 (2009); Talipova T G, Pelinovsky E N, Petrukhin N S Oceanology 49 622 (2009)
  22. Gossard E E, Hooke W H Waves In The Atmosphere (Amsterdam: Elsevier, 1975); Gossard E, Khuk U Volny Atmosfere (1978)
  23. Schoenberg M, Sen P N J. Acoust. Soc. Am. 73 61 (1985)
  24. Artan R, Altan B S Int. J. Solids Struct. 39 5927 (2002)
  25. Guck J et al. Phys. Rev. Lett. 84 5451 (2000)
  26. Aleshin , Gusev V, Tournat V J. Acoust. Soc. Am. 121 2600 (2007)
  27. Eikhenval’d A A Zhurn. Russk. Fiz.-khim. Obshchestva Ch. Fiz. 41 131 (1909)
  28. Mandelstam L I, Zeleni P Ann. Phys. 31 58 (1910)
  29. Gamow G Z. Phys. 51 204 (1928)
  30. Feynman R P, Hibbs A R Quantum Mechanics And Path Integrals (New York: McGraw-Hill, 1965)
  31. Mikhailovskii A B Elektromagnitnye Neustoichivosti Neodnorodnoi Plazmy (M.: Energoatomizdat, 1991); Mikhailovskii A M Electromagnetic Instabilities In An Inhomogeneous Plasma (Bristol: IOP Publ., 1992)
  32. Shvartsburg A B, Petite G Opt. Lett. 31 1127 (2006)
  33. Shalaev V M Nature Photon. 1 41 (2007)
  34. Shvartsburg A B et al. Phys. Rev. E 78 016601 (2008)
  35. Eisner E J. Acoust. Soc. Am. 41 1126 (1967)
  36. Webster A G J. Audio Eng. Soc. 25 24 (1977)
  37. Forbes B J Phys. Rev. E 72 016627 (2005)
  38. Rudenko O V, Shvartsburg A B Akust. Zhurn. (2010), v pechati
  39. Chen H, Chan C T Appl. Phys. Lett. 91 183518 (2007)
  40. Bliokh K Yu, Bliokh Yu P Usp. Fiz. Nauk 174 439 (2004); Bliokh K Yu, Bliokh Yu P Phys. Usp. 47 393 (2004)
  41. Cummer S A et al. Phys. Rev. Lett. 100 024301 (2008)
  42. Jackson J D Classical Electrodynamics 3rd ed. (New York: Wiley, 1999); Dzhekson Dzh Klassicheskaya Elektrodinamika (M.: Mir, 1965)
  43. Godin O A J. Acoust. Soc. Am. 125 EL117 (2009)
  44. Brekhovskikh L M, Godin O A Acoustics Of Layered Media II: Point Sources And Bounded Beams 2nd ed. (Berlin: Springer, 1999)
  45. Biryukov S V Poverkhnostnye Akusticheskie Volny v Neodnorodnykh Sredakh (M.: Nauka, 1991)
  46. Chen C-H et al. Phys. Rev. Lett. 103 238101 (2009)
  47. Sluys L J, de Brost R, Mühlhaus H B Int. J. Solids Struct. 30 1153 (1993)
  48. Dubinov A E, Mytareva L A Usp. Fiz. Nauk 180 475 (2010); Dubinov A E, Mytareva L A Phys. Usp. 53 455 (2010)
  49. Norris A N Proc. R. Soc. London A 464 2411 (2008)
  50. Farhat M et al. Phys. Rev. Lett. 101 134501 (2008)
  51. Milton G W New J. Phys. 9 359 (2007)
  52. Leonhardt U Science 312 1777 (2006)
  53. Gurbatov S N, Rudenko O V, Saichev A I Volny i Struktury v Nelineinykh Sredakh bez Dispersii (M.: Fizmatlit, 2008)
  54. Erokhin N S, Mikhailovskaya L A, Shalimov S L Geofiz. Issled. (7) 53 (2007)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions