In the theory of plane inhomogeneous elastic waves, the complex wave vector constituted by two real vectors in a given plane may be described with the aid of two complex scalar parameters. Either of those parameters may be taken as a free one in the characteristic condition assigned to the wave equa
Erratum to “On the theory of plane inhomogeneous waves in anisotropic elastic media” [Wave Motion 34 (2001) 401–429]
✍ Scribed by A.L. Shuvalov
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 24 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0165-2125
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✦ Synopsis
The publisher regrets that when the above article was printed, there were a series of typographical errors in the text. These errors are listed below.
The third from the top paragraph on p. 424 should read as follows.
Evidently, the manifold of p, λ-degeneracy, identified above as a one-dimensional real domain in R 6 or C 3 , may occur either as a joint border of the manifolds of p-degeneracy and λ-degeneracy (dimensions 3 and 2, respectively) or as a detached manifold. Because p-degeneracy and λ-degeneracy are non-semisimple, their coalescence should be expected to produce p, λ-degeneracy also of the non-semisimple type. This type cannot occur for real p (bulk waves), hence it follows, firstly, that the manifolds of p-degeneracy and λ-degeneracy are unlikely to meet each other at real p, and, secondly, that stable acoustic axes should belong to the detached manifold of p, λ-degeneracy where both non-semisimple and semisimple degeneracy types are admitted. However, the most significant attribute of p, λ-degeneracy is that its detached manifold can occur within the domains of analytical dispersion dependencies given by the characteristic equation ( 5) (in contrast to p-degeneracy and λ-degeneracy, which are associated with locally non-analytical dependencies p 1, 2 (λ) and λ 1, 2 (p), see Section 3.1). This observation underlies an effective strategy of finding and analyzing p, λ-degeneracy in a given elastic medium, as will be discussed next.
On pp. 413 (1st line below Eq. ( 75)) and 427 (5th and 8th lines of the last but one paragraph), 'p, λ-degeneracy' should be replaced by 'p-degeneracy and λ-degeneracy', and on p. 424 (6th line from the bottom) 'λ-and p-degeneracy' should also be replaced by 'p-degeneracy and λ-degeneracy'. The first term under radical in Eq. ( 74) is
The second sentence below Eq. ( 92) implies '15 degree in p'.
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