A new use of the elastodynamic reciprocity theorem

Jan D. Achenbach*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


For an isotropic linearly elastic half-space whose elastic moduli and mass density depend on the distance from the free surface, the surface wave motion radiating from a time-harmonic point load applied normal to the surface of the half-space is considered in this paper. The surface wave velocity, which depends on the wave number, together with expressions for the displacements and stresses of free surface waves, are obtained in a high-frequency approximation. Application of the reciprocity theorem using general expressions for the surface wave radiated by the oscillating point load, together with a virtual free surface wave, yields relatively simple expressions for the amplitude factor of the radiated surface wave. For a few examples, results show the velocity of surface waves and the amplitude factor of the surface waves as a function of the wave number.

Original languageEnglish (US)
Pages (from-to)5-18
Number of pages14
JournalMathematics and Mechanics of Solids
Issue number1
StatePublished - Jan 2014


  • Surface waves
  • depth dependent properties
  • reciprocity theorem

ASJC Scopus subject areas

  • General Mathematics
  • General Materials Science
  • Mechanics of Materials


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