1. Challenges in Hydrodynamic Analysis of VLFS M.Ohkusu ohkusu@jamstec.go.jp Workshop on Very Large Floating Structures for the Future Trondheim 28-29 October 2004

2. Challenges Non-uniformity Station-keeping Consequence of small failure Local phenomena Small global rigidity

3. X Y h d Fluid beneath the platform Fluid without the platform above Thin plate type:

6. x Frequency of resonance of 1D vibration: Eqs of vibration Eq. of wave number b-b Thin plate type:

7. Complex frequency of resonance for a plate(Meylan 2003)

8. Energy of plate vibration (Meylan 2003)

9. Transmission T and reflection R coefficients of a plate (Meylan 2003)

10. Reflection coefficient is zero at

11. x y b -b Frequency of resonance of 2D vibration Periodic in Y direction Thin plate type:

12. x y b -b : progressive wave impossible : trapped-mode no incident wave

13. x y b -b : progressive wave impossible : trapped-mode no incident wave

14. Complex frequency of resonance (2nd symmetric mode) (Tkhacheva 2000 )

15. Complex frequency of resonance (2nd asymmetric mode) (Tkhacheva 2000 )

16. Geometrical optics approach plate water Parabolic approximation

17. Deflection of a Plate in Oblique Waves at 65.2deg Less Than the Critical Angle (shallow water)

19. Comparison of Analytical and Numerical Solutions Analytical Numerical

20. Analytical Deflection: Numerical

21. Ray approach Full numerical ( Ohmatsu ) Oblique incidence ( Takagi )

23. Hierarchical Interaction Theory (Kashiwagi) A trouble: Fictitious bodies must not penetrate each other Float array

24. Wave Pattern around a column-supported VLFS N=32X160(d/a=2) N=16X80(d/a=1) In a wave of L/λ=32.59 coming from upper right

25. Experiment (Kashiwagi)

26. Wave elevation between floats

27. Wave exciting surge & heave forces

29. Steady Wave Drift Force ; inside(left) & outside (right)

30. x y b -b : progressive wave impossible : trapped-mode no incident wave

31. Complex frequency of resonance (2nd symmetric mode) (Tkhacheva 2000 )

32. Complex frequency of resonance (2nd asymmetric mode) (Tkhacheva 2000 )

33. Geometrical optics approach plate water Parabolic approximation

34. Deflection of a Plate in Oblique Waves at 65.2deg Less Than the Critical Angle (shallow water)

36. Comparison of Analytical and Numerical Solutions Analytical Numerical

37. Analytical Deflection: Numerical

38. Ray approach Full numerical ( Ohmatsu ) Oblique incidence ( Takagi )

40. Hierarchical Interaction Theory (Kashiwagi) A trouble: Fictitious bodies must not penetrate each other Float array

41. Wave Pattern around a column-supported VLFS N=32X160(d/a=2) N=16X80(d/a=1) In a wave of L/λ=32.59 coming from upper right

42. Experiment (Kashiwagi)

43. Wave elevation between floats

44. Wave exciting surge & heave forces

46. Steady Wave Drift Force ; inside(left) & outside (right)