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Beating vibration phenomenon of a very large floating structure

Original article
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Abstract

When a very large floating structure (VLFS) is subjected to successive regular waves, it may sometimes suffer from “beating vibration”. This phenomenon occurs when the wave period approaches the natural periods of the structure. The beating action occurs with the period far longer than the incident wave period and sometimes has a conspicuous ups and downs. The vibration amplitude due to regular wave will be alternatively increased and decreased as the synergistic effect caused by the beating. The mechanism of the beating vibration has been investigated through FEM simulation based on the time-domain analysis then the example cases of beating phenomena are demonstrated focusing on the VLFS which was preliminarily designed as a supply base for a deep ocean. It has turned out that the fundamental characteristics of the beating action are mainly contributed by the magnitude of period gap between the incident wave and the natural period of the structure, and also by the magnitude of the damping force.

Keywords

VLFS Beating vibration Lower-hull element float Time-domain analysis Waveless period 

Abbreviations

Tw

Wave period

λ

Wave length

Hw

Wave height

H1/3

Significant wave height

u

Velocity of the water particle

wx, wy, wz

Displacement components associated with x, y and z axes

Lup, Bup, Dup

Length, breadth, depth of the upper structure of LH-600

Dall, d

Depth and draft of the whole body of LH-600

Le, Be, De

Length, breadth, depth of the lower-hull element structure of LH-600

Δ, Δe

Displacement of LH-600 and the lower-hull element float

Se

Sectional area of the lower-hull element float

h

Water depth at the site

Fex, fx

Surge exciting force and its coefficient for the lower-hull element

Fez, fz

Heave exciting force and its coefficient for the lower-hull element

Mey, my

Exciting moment and its coefficient for the lower-hull element

ρ

Density of sea water

tsh

Shell plate thickness of the modified upper structure

ζa

Amplitude of incident wave

Ae, a

Added mass and its coefficient for the lower-hull element

Aex, ax

Added mass and its coefficient associated with surge motion

Aez, az

Added mass and its coefficient associated with heave motion

Ce, c

Wave making damping force and its coefficient for the lower-hull element

Cex, cx

Wave making damping force and its coefficient associated with surge motion

Cez, cz

Wave making damping force and its coefficient associated with heave motion

ke

Static restoring force coefficient for the column element

Sw

Sectional area of water plane for the lower-hull element

χ

Wave incident angle (head sea: χ = 0 deg.)

M, A

Matrix for structural mass and added mass

C

Wave making damping matrix

K

Matrix for structural rigidity and static restoring force

F

External force matrix

D, De

Drag force matrix and the drag force for the lower-hull element

Cd

Drag coefficient

KC

Keulegan Carpenter number

σxb, σxa

Bending stress and axial stress on the upper deck

Mxb

Bending moment of the upper structure

Z

Section modulus of the upper structure

σY

Yield stress of the material

TB

Beating period

Ph_FORE

Phase-lag of the heave displacement at Node 497

Notes

Acknowledgements

The authors are grateful to the former members of ocean engineering division of Ship Research Institute (presently, National Maritime Research Institute) for their research achievements [11]. The data regarding the hydrodynamic characteristics of the lower-hull element floats was borrowed from their works.

References

  1. 1.
    Kobayashi K et al (2001) On-sea experimental results of the Mega-float phase-II model (in Japanese). In: Proceedings of 16th Ocean engineering symposium, The Japan society of naval architects and ocean engineers, pp 11–418Google Scholar
  2. 2.
    Ohta M et al (2001) Hydroelastic response of mega-float phase-II model in waves (in Japanese). In: Proceedings of 16th ocean engineering symposium, The Japan society of naval architects and ocean engineers, pp 419–424Google Scholar
  3. 3.
    Kinoshita Y, Kado M (2000) Outline of construction and corroborative experiments of the floating airport model for the Mega-float R&D program phase II (in Japanese). In: Proceedings of 15th ocean engineering symposium, The Japan society of naval architects and ocean engineers, pp. 45–54Google Scholar
  4. 4.
    Endo H (2000) The behavior of a VLFS and an airplane during takeoff/landing in wave condition. Mar Struct 13:477–491CrossRefGoogle Scholar
  5. 5.
    Yoshida K, Suzuki H et al (2001) A basic study for practical use of semisub-Megafloat (in Japanese). In: Proceedings of 16th ocean engineering symposium, The Japan society of naval architects and ocean engineers, pp 235–240Google Scholar
  6. 6.
    Kobayashi K et al (2000) Hydroelastic behavior of a very large semi-submersible type floating airport in waves (in Japanese). In: Proceedings of 15th ocean engineering symposium, The Japan society of naval architects and ocean engineers, pp 207–214Google Scholar
  7. 7.
    Ministry of Land, Infrastructure, Transport and Tourism (2013) Outline of technological research association of J-DeEP (in Japanese). http://www.mlit.go.jp/common/001013420.pdf
  8. 8.
    Harada T, Maeda K (2015) Feasibility study on logistics hub system for passengers in offshore Brazil (in Japanese). In: Conference proceedings The Japan society of naval architects and ocean engineers, vol 20, pp 349–351Google Scholar
  9. 9.
    Japan Oil, Gas and Metals National Corporation (2013) Handbook of offshore engineering (in Japanese), 5th ednGoogle Scholar
  10. 10.
    Koyama T, Fujino M, Maeda H (2010) Motion of ships and offshore structures (in Japanese), Seizando-shoten publishing, TokyoGoogle Scholar
  11. 11.
    Ando S et al (1985) Research on the fundamental constructing technology for large floating structures (in Japanese). In: Papers of ship research institute, Supplement No. 6, Ship research institute (former name of National maritime research institute)Google Scholar
  12. 12.
    Endo H, Suzuki H (2015) The beating vibration of VLFS. In: Conference proceedings The Japan society of naval architects and ocean engineers, vol 20, pp 79–82Google Scholar
  13. 13.
    Endo H (2015) Application of time domain analysis to hydroelastic behavior of very large floating structures (in Japanese), Doctoral thesis submitted to the university of TokyoGoogle Scholar
  14. 14.
    Kudo K (1983) Keulegan Carpenter number (in Japanese), The Japan society of naval architects and ocean engineers, No. 652, p 59Google Scholar

Copyright information

© JASNAOE 2017

Authors and Affiliations

  1. 1.Formerly, National Maritime Research InstituteMitaka-cityJapan
  2. 2.Department of Ocean Technology, Policy, and Environment, Graduate School of Frontier SciencesThe University of TokyoTokyoJapan

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