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Band structure properties of elastic waves propagating in the nanoscaled nearly periodic layered phononic crystals

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Abstract

The localization factor is used to describe the band structures for P wave propagating normally in the nanoscaled nearly periodic layered phononic crystals. The localization factor is calculated by the transfer matrix method based on the nonlocal elastic continuum theory. Three kinds of nearly periodic arrangements are concerned, i.e., random disorder, quasi-periodicity and defects. The influences of randomly disordered degree of the sub-layer’s thickness and mass density, the arrangement of quasi-periodicity and the location of defect on the band structures and cut-off frequency are analyzed in detail.

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References

  1. M.S. Kushwaha, P. Halevi, G. Martinez, L. Dodrzynski, B. Djafarirouhani, Acoustic band structure of periodic elastic composites, Phys. Rev. Lett. 71 (1993) 2022–2025.

    Article  Google Scholar 

  2. P.W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109 (1958) 1492–1505.

    Article  Google Scholar 

  3. O. Barco, M. Ortuno, Localization length of nearly periodic layered metamaterials, Phys. Rev. A 86 (2) (2012) 023846.

    Article  Google Scholar 

  4. H. Gleiter, Nanocrystalline materials, Prog. Mater. Sci. 33 (1989) 223–315.

    Article  Google Scholar 

  5. H. Gleiter, Nanostructured materials: basic concepts and microstructure, Acta Mater. 48 (2000) 1–29.

    Article  Google Scholar 

  6. S.G. Du, D.M. Shi, H. Deng, Special effects and applications of nanostructured materials, Ziran Zazhi 22 (2) (2000) 101–106.

    Google Scholar 

  7. R. Ramprasad, N. Shi, Scalability of phononic crystal hetero structures, Appl. Phys. Lett. 87 (11) (2005) 111101.

    Article  Google Scholar 

  8. S.P. Hepplestone, G.P. Srivastava, Hypersonic modes in nanophononic semiconductors, Phys. Rev. Lett. 101 (10) (2008) 105502.

    Article  Google Scholar 

  9. G.L. Huang, C.T. Sun, Modeling heterostructures of nano-phononic crystals by continuum model with microstructures, Appl. Phys. Lett. 88 (2006) 261908.

    Article  Google Scholar 

  10. G.L. Huang, C.T. Sun, Continuum modelling of solids with micro/nanostructures, Philos. Mag. 87 (2007) 3689–3707.

    Article  Google Scholar 

  11. A.C. Eringen, Theory of micropolar plates, J. Appl. Math. Phys. 18 (1) (1967) 12–30.

    Article  Google Scholar 

  12. A.C. Eringen, Nonlocal polar elastic continua, Int. J. Eng. Sci. 10 (1) (1972) 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  13. M.E. Gurtin, J. Weissmüller, F. Larche, A general theory of curved deformable interfaces in solids at equilibrium, Philos. Mag. A 78 (5) (1998) 1093–1109.

    Article  Google Scholar 

  14. E.C. Aifantis, Strain gradient interpretation of size effects, Int. J. Fract. 95 (1–4) (1999) 299–314.

    Article  Google Scholar 

  15. F. Yang, A.C.M. Chong, D.C.C. Lam, P. Yong, Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct. 39 (10) (2002) 2731–2743.

    Article  MATH  Google Scholar 

  16. Q. Wang, V.K. Varadan, Vibration of carbon nanotubes studied using nonlocal continuum mechanics, Smart Mater. Struct. 15 (2) (2006) 659–662.

    Article  Google Scholar 

  17. R. Ansari, A. Shahabodini, H. Rouhi, Prediction of the biaxial buckling and vibration behavior of graphene via a nonlocal atomistic-based plate theory, Compos. Struct. 95 (2013) 88–94.

    Article  Google Scholar 

  18. L.L. Ke, Y.S. Wang, Thermo-electric-mechanical vibration of the piezoelectric nanobeams based on the nonlocal theory, Compos. Struct. 77 (12) (2012) 2031–2042.

    Google Scholar 

  19. C. Liu, L.L. Ke, Y.S. Wang, J. Yang, S. Kitipornchai, Thermo-electro-mechanical vibration of piezoelectric nanoplates based on the nonlocal theory, Compos. Struct. 106 (2013) 167–174.

    Article  Google Scholar 

  20. Y.G. Hu, K.M. Liew, Q. Wang, X.Q. He, B.I. Yakobson, Nonlocal shell model for elastic wave propagation in single-and double-walled carbon nanotubes, J. Mech. Phys. Solids 56 (12) (2008) 3475–3485.

    Article  MATH  Google Scholar 

  21. H. Heireche, A. Tounsi, A. Benzair, M. Maachou, E.A.Adda Bedia, Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity, Phys. E: Low-Dimens. Syst. Nanostruct. 40 (8) (2008) 2791–2799.

    Article  Google Scholar 

  22. L.L. Zhang, J.X. Liu, X.Q. Fang, G.Q. Nie, Effects of surface piezoelectricity and nonlocal scale on wave propagation in piezoelectric nanoplates, Eur. J. Mech. A: Solids 46 (8) (2014) 22–29.

    Article  Google Scholar 

  23. A.L. Chen, Y.S. Wang, Size-effect on band structures of nanoscale phononic crystals, Phys. E: Low-Dimens. Syst. Nanostruct. 44 (1) (2011) 317–321.

    Article  Google Scholar 

  24. A.L. Chen, Y.S. Wang, L.L. Ke, Y.F. Guo, Z.D. Wang, Wave propagation in nanoscaled periodic layered structures, J. Comput. Theor. Nanosci. 10 (10) (2013) 2427–2437.

    Article  Google Scholar 

  25. A.L. Chen, D.J. Yan, Y.S. Wang, Ch. Zhang, Anti-plane transverse waves propagation in nanoscale periodic layered piezoelectric structures, Ultrasonics 65 (2016) 154–164.

    Article  Google Scholar 

  26. D.G.B. Edelen, N. Laws, On the thermodynamics of systems with nonlocality, Arch. Ration. Mech. Anal. 43 (1) (1971) 24–35.

    Article  MathSciNet  MATH  Google Scholar 

  27. A.C. Eringen, D.G.B. Edelen, On nonlocal elasticity, Int. J. Eng. Sci. 10 (3) (1972) 233–248.

    Article  MathSciNet  MATH  Google Scholar 

  28. A.C. Eringen, Non-local polar field theories, Continuum Physics, Academic Press, New York, 1976, pp. 205–267.

    Google Scholar 

  29. D.G.B. Edelen, Nonlocal field theories, Continuum Physics, Academic Press, New York, 1976, pp. 75–204.

    Google Scholar 

  30. A.C. Eringen, Nonlocal Continuum Field Theories, Springer-Verlag, New York, 2002.

    MATH  Google Scholar 

  31. Z.G. Liu, Research of Application of Nonlocal theory, Micropolar Theory on Problems of Elastic Waves and Fracture, Harbin Institute of Technology, 1992.

  32. A.L. Chen, Y.S. Wang, Study on band gaps of elastic waves propagating in one-dimensional disordered phononic crystals, Physica B 392 (2007) 369–378.

    Article  Google Scholar 

  33. A.L. Chen, Y.S. Wang, Y.F. Guo, Z.D. Wang, Band structures of Fihonacci phononic quasi crystals, Solid State Commun. 145 (2008) 103–108.

    Article  Google Scholar 

  34. W.C. Xie, A. Ibrahim, Buckling mode localization in rib-stiffened plates with misplaced stiffeners—a finite strip approach, Chaos Solitons Fractals 11 (2000) 1543–1558.

    Article  MATH  Google Scholar 

  35. A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Determining Lyapunov exponents from a time series, Physica D 16 (1985) 285–317.

    Article  MathSciNet  MATH  Google Scholar 

  36. G.J. Kissel, Localization factor for multichannel disordered systems, Phys. Rev. A 44 (1991) 1008–1014.

    Article  Google Scholar 

  37. R. Merlin, K. Bajema, R. Clarke, F.Y. Juang, P.K. Bhattacharga, Quasiperiodic GaAs–AlAs heterostructures, Phys. Rev. Lett. 55 (1985) 1768–1770.

    Article  Google Scholar 

  38. A. Hu, S.S. Jiang, R.W. Peng, C.S. Zhang, D. Feng, Extended one-dimensional Fibonacci structures, Acta Phys. Sin. 41 (1) (1992) 62–68.

    Google Scholar 

  39. Y. Lu, R.W. Peng, Z. Wang, Z.H. Tang, X.Q. Huang, M. Wang, Y. Qiu, A. Hu, S.S. Jiang, D. Feng, Resonant transmission of light waves in dielectric heterostructures, J. Appl. Phys. 97 (2005) 123106.

    Article  Google Scholar 

  40. R.W. Peng, X.Q. Huang, F. Qiu, M. Wang, A. Hu, S.S. Jiang, Symmetry- induced perfect transmission of light waves in quasiperiodic dielectric multilayers, Appl. Phys. Lett. 80 (2002) 3063–3065.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing, 100044, China

    A-Li Chen, Li-Zhi Tian & Yue-Sheng Wang

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  1. A-Li Chen
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  2. Li-Zhi Tian
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  3. Yue-Sheng Wang
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Correspondence to A-Li Chen.

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Chen, AL., Tian, LZ. & Wang, YS. Band structure properties of elastic waves propagating in the nanoscaled nearly periodic layered phononic crystals. Acta Mech. Solida Sin. 30, 113–122 (2017). https://doi.org/10.1016/j.camss.2017.03.005

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