On the acoustic determination of the elastic moduli of anisotropic solids and acoustic conditions for the existence of symmetry planes

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Abstract

The twenty-one elastic moduli of a homogeneous anisotropic solid can be determined from the second-order acoustical tensors associated with wave motion in six phase directions. The directions may be quite arbitrary as long as they cannot be contained by less than three distinct planes through the origin and do not all lie on the curves formed by the intersection of the unit sphere with an elliptical cone. Two equivalent sets of conditions necessary and sufficient for the existence of a plane of material symmetry in an elastic solid are presented. The conditions are phrased in terms of acoustic waves, the first set involving polarization vectors, the second energy-flux vectors. Some consequences of the acoustic conditions are noted.

Original languageEnglish (US)
Pages (from-to)413-426
Number of pages14
JournalQuarterly Journal of Mechanics and Applied Mathematics
Volume42
Issue number3
DOIs
StatePublished - Aug 1989

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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