Dispersive behavior of high frequency Rayleigh waves propagating on an elastic half space

Abstract

When the wavelength of Rayleigh wave is comparable with nanometers, Rayleigh wave will become dispersive. Such an interesting phenomenon cannot be predicted by the classical theory of elastodynamics. In order to reveal the internal mechanism and influencing factors of the dispersion, a model of Rayleigh wave propagating on an elastic half space is established and analyzed by a new theory of surface elastodynamics, in which the surface effect characterized by both the surface energy density and surface inertia is introduced. Two intrinsic nano-length scales, including the ratio of bulk surface energy density to bulk shear modulus and the ratio of surface mass density to bulk mass density, are achieved. It is found that when the wavelength of Rayleigh wave is comparable with the two intrinsic nano-lengths, the surface effect becomes significant. As a result, dispersion of Rayleigh wave happens and even two Rayleigh waves with different wave speeds may appear. Furthermore, it is found that the effect of surface energy density would enhance the wave speed, while that of surface inertia would reduce it. With the increase of wavelength, both effects gradually disappear and the Rayleigh wave speed degenerates to the classical one. The results of this paper are not only helpful to understand the dispersive mechanism of elastic waves, but also helpful for the fine design and measurement of nanowave devices.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 11532013, 11872114, 11772333, and 12002033) and the Project of State Key Laboratory of Explosion Science and Technology (Grant ZDKT17-02).

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Correspondence to Yin Yao or Shaohua Chen.

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Jia, N., Peng, Z., Li, J. et al. Dispersive behavior of high frequency Rayleigh waves propagating on an elastic half space. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-020-01009-3

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Keywords

  • Rayleigh wave
  • High frequency
  • Dispersion
  • Elastodynamics
  • Surface effect