Propagation of a surface wave near a randomly rough surface

Authors

  • Anatoly V. Chigarev Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
  • Marina G. Botogova Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
  • Gennadi I. Mikhasev Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Keywords:

elastic Rayleigh wave, dispersion of surface roughness, small dimensionless parameter
Supporting Agencies
This work was supported by the state program of scientific research «Convergence-2025» (task 1.7.01.2).

Abstract

A generalisation of the problem on the propagation of a surface elastic Rayleigh wave near a free surface obtained by continuous deformation of the initial plane is considered. The set of possible realisations of the surface is, on average, equivalent to a plane, and the dispersion is a constant. The smallness of a dimensionless parameter, the gradient to a surface, is assumed, which causes the presence of small fluctuations in all field quantities. The effective boundary conditions on a plane boundary are obtained. From the condition for the existence of non-zero solutions, the generalised Rayleigh equation is found for the case of an uneven boundary containing a parameter of a dimensionless dispersion of the gradient to a surface. Roots of the dispersion equation are numerically found depending on the Poisson’s ratio and dispersion. The influence of the dispersion of surface roughness is manifested in the appearance of an additional root under the condition that the ratio of the Rayleigh wave velocity to the transverse velocity is less than unity. The second root corresponds to the appearance of a wave slower than the Rayleigh one, the amplitude of which also decreases with depth. Physically acceptable solutions can only exist for a dispersion value of less than 0.09 in the range of varying of material properties from solid to rubbery.

Author Biographies

  • Anatoly V. Chigarev, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    doctor of science (physics and mathematics), full professor; professor at the department of bio- and nanomechanics, faculty of mechanics and mathematics

  • Marina G. Botogova, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    PhD (physics and mathematics); associate professor at the department of bio- and nanomechanics, faculty of mechanics and mathematics

  • Gennadi I. Mikhasev, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    doctor of science (physics and mathematics), full professor; head of the department of bio- and nanomechanics, faculty of mechanics and mathematics

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Published

2023-03-27

Issue

No. 1 (2023): Journal of the Belarusian State University. Mathematics and Informatics

Section

Theoretical and Applied Mechanics

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How to Cite

[1]
Chigarev, A.V. et al. 2023. Propagation of a surface wave near a randomly rough surface. Journal of the Belarusian State University. Mathematics and Informatics. 1 (Mar. 2023), 38–48. DOI:https://doi.org/10.33581/2520-6508-2023-1-38-48.