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Acta Mechanica

, Volume 230, Issue 3, pp 805–820 | Cite as

Influences of interface properties on the wave propagation in the dipolar gradient elastic solid

  • Yueqiu LiEmail author
  • Peijun Wei
Original Paper
  • 54 Downloads

Abstract

The present work mainly focuses on the influence of interface material parameters, namely the interface mass density, the interface elastic rigidity, and the interface inertial interaction constants, on the reflection and transmission behavior of elastic wave propagating through dipolar gradient elastic solids. First, the interface kinetic energy density and interface deformation energy density are taken into account. By application of Hamilton’s variation principle, the governing equations and the boundary conditions of the dipolar gradient elastic solid are obtained. Due to the consideration of microstructure effects of the material, the interface conditions can be proposed in different forms. These interfacial conditions which include the microstructure effects and interface energy effects are then used to determine the amplitude ratio of reflection and transmission waves. A numerical example is provided for the generalized internal roller interface. The influence of the interface material parameters upon the reflection and transmission coefficients in terms of energy fluxes ratio is discussed based on the numerical results. It is revealed that the reflection and transmission behavior can be manipulated by the elaborated design of the interface at both the macroscale and the microscale.

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Notes

Acknowledgements

The work is supported by Fundamental Research Funds for the Central Universities (FRF-BR-15-026A), the National Natural Science Foundation of China (No. 10972029), the Fundamental Research Funds in HeiLongJiang Provincial Universities (No. 135109232).

References

  1. 1.
    Andreaus, U., dell’Isola, F., Giorgio, I., Placidi, L., Lekszycki, T., Rizzi, N.L.: Numerical simulations of classical problems in two-dimensional (non) linear second gradient elasticity. Int. J. Eng. Sci. 108, 34–50 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Duan, H.L., Wang, J., Huang, Z.P., Karihaloo, B.L.: Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J. Mech. Phys. Solids 53, 1574–1596 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Dell’Isola, F., Madeo, A., Placidi, L.: Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D Continua. ZAMM-Z. Angew. Math. Mech. 92, 52–71 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Georgiadis, H.G., Vardoulakis, I., Lykotrafitis, G.: Torsional surface waves in a gradient-elastic half-space. Wave Motion 31, 333–348 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Georgiadis, H.G.: The Mode III Crack Problem in microstructured solids governed by dipolar gradient elasticity: static and dynamic analysis. ASME J. Appl. Mech. 70, 517–530 (2003)CrossRefzbMATHGoogle Scholar
  6. 6.
    Georgiadis, H.G., Vardoulakis, I., Velgaki, E.G.: Dispersive Rayleigh-wave propagation in microstructured solids characterized by dipolar gradient elasticity. J. Elast. 74, 17–45 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gourgiotis, P.A., Georgiadis, H.G., Neocleous, I.: On the reflection of waves in half-spaces of microstructured materials governed by dipolar gradient elasticity. Wave Motion 50, 437–455 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Li, Y.Q., Wei, P.J.: Reflection and transmission of plane waves at the interface between two different dipolar gradient elastic half-spaces. Int. J. Solids Struct. 56–57, 194–208 (2015)CrossRefGoogle Scholar
  9. 9.
    Li, Y.Q., Wei, P.J., Tang, Q.H.: Reflection and transmission of elastic waves at the interface between two gradient-elastic solids with surface energy. Eur. J. Mech. A Solids 52, 54–71 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Li, Y.D., Lee, K.Y.: Effect of an imperfect interface on the SH wave propagating in a cylindrical piezoelectric sensor. Ultrasonics 50, 473–478 (2010)CrossRefGoogle Scholar
  11. 11.
    Li, P., Jin, F.: Excitation and propagation of shear horizontal waves in a piezoelectric layer imperfectly bonded to a metal or elastic substrate. Acta Mech. 226, 267–284 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Mindlin, R.D.: Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51–78 (1964)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Miller, R.E., Shenoy, V.B.: Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11, 139–147 (2000)CrossRefGoogle Scholar
  14. 14.
    Murdoch, A.I.: The propagation of surface waves in bodies with material boundaries. J. Mech. Phys. Solids 24, 137–146 (1976)CrossRefzbMATHGoogle Scholar
  15. 15.
    Nyayadhish, V.B.: Elastic shear waves in the presence of couple stresses. Acta Phys. Acad. Sci. Hung. Tomus 41, 19–27 (1976)CrossRefGoogle Scholar
  16. 16.
    Placidi, L., Rosi, G., Giorgio, I., Madeo, A.: Reflection and transmission of plane waves at surfaces carrying material properties and embedded in second-gradient materials. Math. Mech. Solids 19, 555–578 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Parfitt, V.R., Eringen, A.C.: Reflection of plane waves from the flat boundary of a micropolar half-space. J. Acoust. Soc. Am. 45, 1258–1272 (1969)CrossRefGoogle Scholar
  18. 18.
    Nagy, P.B.: Ultrasonic classification of imperfect interfaces. J. Nondestruct. Eval. 11, 127–139 (1992)CrossRefGoogle Scholar
  19. 19.
    Rosi, G., Placidi, L., Nguyen, V.H., Salah, N.: Wave propagation across a finite heterogeneous interphase modeled as an interface with material properties. Mech. Res. Commun. 84, 43–48 (2017)CrossRefGoogle Scholar
  20. 20.
    Tomar, S.K., Gogna, M.L.: Reflection and refraction of longitudinal wave at an interface between two micropolar elastic solids at welded contact. J. Acoust. Soc. Am. 97, 822–830 (1995)CrossRefzbMATHGoogle Scholar
  21. 21.
    Tomar, S.K., Garg, M.: Reflection and transmission of waves from a plane interface between two microstretch solid half-spaces. Int. J. Eng. Sci. 43, 139–169 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Vardoulakis, I., Georgiadis, H.G.: SH surface waves in a homogeneous gradient-elastic half-space with surface energy. J. Elast. 47, 147–165 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Yerofeyev, V.I., Sheshenina, O.A.: Waves in gradient-elastic medium with surface energy. J. Appl. Math. Mech. 69, 57–59 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsQiqihar UniversityQiqiharChina
  2. 2.Department of Applied MechanicsUniversity of Science and Technology BeijingBeijingChina

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