Application of the reciprocity theorem to determine line-load-generated surface waves on an inhomogeneous transversely isotropic half-space

Salil S. Kulkarni*, Jan Drewes Achenbach

*Corresponding author for this work

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

Free and forced time-harmonic surface waves are investigated for a half-space of transversely isotropic elastic material, where the axis normal to the free surface (the z-axis) is the axis of symmetry. In addition, the elastic constants and the mass density depend on the distance from the free surface. A surface wave is considered as being composed of a carrier wave that propagates over the free surface as it would over a membrane, while it carries along a system of depth-dependent motions. For free surface waves the analytical details, i.e., the calculation of the wave speed of the free surface waves, are worked out for the case that the elastic constants and the mass density vary exponentially with depth. For forced motion by a time-harmonic line load, the far-field surface wave motion is determined by an application of the reciprocity theorem for elastodynamics. Numerical results for displacements and stresses are graphically displayed. Fourier superposition has been used to determine the transient surface wave response to a pulse-type normal line-load.

Original languageEnglish (US)
Pages (from-to)350-360
Number of pages11
JournalWave Motion
Volume45
Issue number3
DOIs
StatePublished - Jan 1 2008

Keywords

  • Inhomogeneous
  • Line load
  • Reciprocity
  • Surface waves
  • Transversely isotropic

ASJC Scopus subject areas

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

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