Bounds and approximations for elastodynamic wave speeds in tetragonal media

Q. H. Zuo, K. D. Hjelmstad

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This paper presents an analytical study of elastodynamic waves propagating along an arbitrary direction in anisotropic materials with tetragonal symmetry. Upper and lower bounds are developed on the wave speeds through an additive decomposition of the acoustic tensor into an associated hexagonal counterpart and a rank-one modification, the eigenproperties of which can be determined analytically. The bounds are obtained by applying the minimax property of eigenvalues. Linear approximations of the wave speeds are obtained from a first-order expansion of the eigenvalues of the acoustic tensor, with respect to a tetragonality index, about the value of that index for which tetragonal symmetry degenerates to hexagonal symmetry. A numerical example shows that the linear approximations agree remarkably well with the exact values of the wave speeds.

Original languageEnglish (US)
Pages (from-to)1727-1733
Number of pages7
JournalJournal of the Acoustical Society of America
Issue number4
StatePublished - Apr 1998
Externally publishedYes

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics


Dive into the research topics of 'Bounds and approximations for elastodynamic wave speeds in tetragonal media'. Together they form a unique fingerprint.

Cite this