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Litian Wang Østfold University College Extraordinary degeneracy and space of degeneracy in transversely isotropic elastic media Litian Wang Østfold University.

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Presentation on theme: "Litian Wang Østfold University College Extraordinary degeneracy and space of degeneracy in transversely isotropic elastic media Litian Wang Østfold University."— Presentation transcript:

1 Litian Wang Østfold University College Extraordinary degeneracy and space of degeneracy in transversely isotropic elastic media Litian Wang Østfold University College 1757 Halden Norway

2 Litian Wang Østfold University College Main goals Relationship between the extraordinary degeneracies and existence of the space of degeneracy The Stroh formalism is applied to the transversely isotropic media. We will show that (a)the space of degeneracy can be regarded as an extension of the static degeneracy. (b) the static degeneracy can span a continuous space of degeneracy in the static limit.

3 Litian Wang Østfold University College Transversely isotropic elastic media TiB 2

4 Litian Wang Østfold University College The Stroh formalism

5 Litian Wang Østfold University College The Stroh formalism Reference plane: Traction: m n

6 Litian Wang Østfold University College The Stroh formalism

7 Litian Wang Østfold University College Transversely isotropic elastic media

8 Litian Wang Østfold University College Transversely isotropic elastic media TiB 2

9 Litian Wang Østfold University College Three symmetrical configurations (m,n) γ-configuration β-configuration α-configuration (Chadwick) φ φ φ φ

10 Litian Wang Østfold University College φ γ-configuration

11 Litian Wang Østfold University College β-configuration (Alshits) φ

12 Litian Wang Østfold University College α-configuration φ φ

13 Litian Wang Østfold University College Space of degneracy in the γ-configuration Characteristic equation: φ

14 Litian Wang Østfold University College Space of degneracy in the β-configuration Characteristic equation: (Shuvalov et al) φ

15 Litian Wang Østfold University College Space of degneracy in the α-configuration Characteristic equation: φ φ

16 Litian Wang Østfold University College Properties of the space of degeneracy p 1 =p 2 =p 3 =i Extraordinary degeneracy Result 1: Evolution of the space of degeneracy αβγ

17 Litian Wang Østfold University College p 1 =p 2 =p 3 =i Semisimple degeneracy Non semisimple degeneracy Extraordinary degeneracy D2 Result 2: Characteristic of the space of degeneracy Properties of the space of degeneracy αβγ

18 Litian Wang Østfold University College Properties of the space of degeneracy Result 3: Existence of the space of degeneracy

19 Litian Wang Østfold University College Properties of the space of degeneracy Result 4: Existence of the space of extraordinary degeneracy p 1 =p 2 =p 3 =i p 1 =p 2 =p 3 ≠i Im p

20 Litian Wang Østfold University College Properties of the space of degeneracy Result 5: Space of degeneracy at the static limit (v=0)

21 Litian Wang Østfold University College Conclusions (a) A space of degeneracy (semisimple) can exist in both supersonic and subsonic regime. (b) A space of degeneracy (nonsemisimple) will end up at a type E1 zero-curvature transonic state. (c) A space of degeneracy (extraordinary) can bifurcate into a number of ordinary spaces of degeneracy. (d) A space of degeneracy can anchor or trespass acoustic axes with same type degeneracy.

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