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Research Papers: Structures and Safety Reliability

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

[+] Author and Article Information
João Pessoa

e-mail: joao.pessoa@mar.ist.utl.pt

Nuno Fonseca

e-mail: nfonseca@mar.ist.utl.pt

C. Guedes Soares

e-mail: guedess@mar.ist.utl.pt
Centre for Marine Technology
and Engineering (CENTEC),
Technical University of Lisbon,
Instituto Superior Técnico,
Av. Rovisco Pais,
1049-001 Lisboa, Portugal

Contributed by the Ocean Offshore and Arctic Engineering Division of ASME for publication in the JOURNALOF OFFSHORE MECHANICSAND ARCTIC ENGINEERING. Manuscript received August 4, 2010; final manuscript received May 8, 2012; published online February 22, 2013. Assoc. Editor: Arvid Naess.

J. Offshore Mech. Arct. Eng 135(1), 011601 (Feb 22, 2013) (11 pages) Paper No: OMAE-10-1081; doi: 10.1115/1.4007045 History: Received August 04, 2010; Revised May 08, 2012

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

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Figures

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Fig. 1

(left) Mesh with 860 lower order panels for one quarter of the wetted surface. The free surface is discretized with 175 panels for a quarter of the domain to allow for the forcing to be integrated. (right) Curve whose 360 deg revolution originates in the wetted surface.

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Fig. 2

(left) Model during a shallow water test. (right) Mooring pole chain system layout to control the line stiffness. The correct stiffness is ensured by the weight per meter of the hanging chain.

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Fig. 3

Surge first order motion response amplitude operators as a function of the incident wave period. Amplitudes normalized by the incident wave amplitude A (water depths of 40, 55, and 300 cm).

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Fig. 4

Heave first order motion response amplitude operators as a function of the incident wave period. Amplitudes normalized by the incident wave amplitude A (water depths of 40, 55, and 300 cm).

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Fig. 5

Pitch first order motion response amplitude operators as a function of the incident wave period. Amplitudes normalized by AL, where A is the incident wave amplitude and L = 1 m (water depths of 40, 55, and 300 cm).

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Fig. 6

Surge steady drift motion offset as function of the incident wave period. Steady motion normalized by A2/L, where A is the incident wave amplitude and L = 1 m.

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Fig. 7

Surge slow drift motion amplitudes as function of the average incident wave period for three water depths and two difference frequencies (dw = 0.5 and 1.5 rad/s). Motion amplitudes normalized by AiAj/L, where Ai, Aj are the amplitudes of the two incident harmonic waves and L = 1 m.

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Fig. 8

Heave slow drift motion amplitudes as a function of the average incident wave period for three water depths and one difference frequency (dw = 0.5 rad/s). Motion amplitudes normalized by AiAj/L, where Ai, Aj are the amplitudes of the two incident harmonic waves and L = 1 m.

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Fig. 9

Pitch slow drift motion amplitudes as a function of the average incident wave period for two water depths and two difference frequencies (dw = 0.5 and

4.0 rad/s). Motion amplitudes normalized by AiAj/L2, where Ai, Aj are the amplitudes of the two incident harmonic waves and L = 1 m.

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