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Extraordinary degeneracy and space of degeneracy in transversely isotropic elastic media

Extraordinary degeneracy and space of degeneracy in transversely isotropic elastic media. Litian Wang Østfold University College 1757 Halden Norway. Main goals. Relationship between the extraordinary degeneracies and existence of the space of degeneracy

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Extraordinary degeneracy and space of degeneracy in transversely isotropic elastic media

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

  2. 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 • 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. Transversely isotropic elastic media TiB2

  4. The Stroh formalism

  5. n m The Stroh formalism Reference plane: Traction:

  6. The Stroh formalism

  7. Transversely isotropic elastic media

  8. Transversely isotropic elastic media TiB2

  9. γ-configuration φ φ φ β-configuration φ α-configuration Three symmetrical configurations (m,n) (Chadwick)

  10. φ γ-configuration

  11. φ β-configuration (Alshits)

  12. φ φ α-configuration

  13. φ Space of degneracy in the γ-configuration Characteristic equation:

  14. φ Space of degneracy in the β-configuration Characteristic equation: (Shuvalov et al)

  15. φ φ Space of degneracy in the α-configuration Characteristic equation:

  16. Properties of the space of degeneracy Result 1: Evolution of the space of degeneracy γ β α p1=p2=p3=i Extraordinary degeneracy

  17. Extraordinary degeneracy D2 Semisimple degeneracy Non semisimple degeneracy Properties of the space of degeneracy Result 2: Characteristic of the space of degeneracy γ β α p1=p2=p3=i

  18. Properties of the space of degeneracy Result 3: Existence of the space of degeneracy

  19. Properties of the space of degeneracy Result 4: Existence of the space of extraordinary degeneracy Im p p1=p2=p3≠i p1=p2=p3=i p1=p2=p3=i

  20. Properties of the space of degeneracy Result 5: Space of degeneracy at the static limit (v=0)

  21. 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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