Reflection of a beam of elastic waves by a periodic surface profile

R. Roberts*, J. D. Achenbach, R. Ko, L. Adler, A. Jungman, G. Quentin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Reflection of elastic waves from a traction-free solid-air boundary of periodic saw-tooth profile is investigated analytically and experimentally. For an incident plane wave the surface displacements on the profile are computed as the solution of a singular integral equation. The reflected field is subsequently obtained by using an integral representation. Incident beams of finite width are represented by Fourier superpositions of plane waves. The dependence of the reflected signal spectra on the incident beam width is examined closely near the fundamental surface resonance frequency. Experimental spectra which were obtained using two different diameter transducers, are compared to the corresponding theoretical spectra. It is found that the depth of the spectral minima depends on the incident beam width. Both analytical and experimental results exhibit the splitting of an incident beam of elastic waves into two reflected beams. The beam splitting is more pronounced for a narrower incident beam and for frequencies close to a resonance frequency of the profile.

Original languageEnglish (US)
Pages (from-to)67-77
Number of pages11
JournalWave Motion
Issue number1
StatePublished - Jan 1985

ASJC Scopus subject areas

  • Modeling and Simulation
  • Physics and Astronomy(all)
  • Computational Mathematics
  • Applied Mathematics


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