Bounds and approximations for elastodynamic wave speeds in tetragonal media

Q. H. Zuo, Keith Hjelmstad

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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
Volume103
Issue number4
DOIs
StatePublished - Apr 1998
Externally publishedYes

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elastodynamics
approximation
symmetry
eigenvalues
tensors
acoustics
decomposition
expansion
Waves
Approximation
Symmetry
Acoustics

ASJC Scopus subject areas

  • Acoustics and Ultrasonics

Cite this

Bounds and approximations for elastodynamic wave speeds in tetragonal media. / Zuo, Q. H.; Hjelmstad, Keith.

In: Journal of the Acoustical Society of America, Vol. 103, No. 4, 04.1998, p. 1727-1733.

Research output: Contribution to journalArticle

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