Scattering of a Rayleigh wave by a near surface crack which is normal to the free surface

Chuanyong Wang, Oluwaseyi Balogun, Jan Drewes Achenbach*

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Scopus citations


In this paper, scattering of a Rayleigh surface wave by a 2D near-surface crack which is normal to the free surface of a homogenous, isotropic and linearly elastic half-space has been investigated. The scattered field is represented by the radiation from equivalent body forces, which are expressed in terms of the crack-opening volumes generated by the incident Rayleigh wave. The reciprocity theorem together with a virtual wave has been used to determine the amplitude of the far field of the scattered Rayleigh wave. A special case of low frequency, and small ratio of the crack length to the wavelength of the incident Rayleigh wave, has been considered to illustrate the method for different values of the ratio of crack length to the wavelength of the incident surface wave. The displacements of the analytical solution on the free surface at some distance from the crack are compared with the displacements obtained numerically. Analytical and numerical results show excellent agreement when the Rayleigh wavelength is sufficiently larger than the crack length. The results of this paper should be useful for the quantitative non-destructive evaluation of a near-surface crack.

Original languageEnglish (US)
Article number103162
JournalInternational Journal of Engineering Science
StatePublished - Dec 1 2019



  • Equivalent body force
  • Near surface crack
  • Rayleigh wave
  • Reciprocity theorem

ASJC Scopus subject areas

  • Materials Science(all)
  • Engineering(all)
  • Mechanics of Materials
  • Mechanical Engineering

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