Computation of springing transfer functions

Söding, H

doi:10.1243/14750902jeme158

Cited by 5 publications

(2 citation statements)

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“…where_ j9 (i) andṽ9 (i) (i = 1, 2) are the translatory and angular velocity vectors of the body expressed in the body-fixed coordinate system.Ũ9 (k) (k = 1, 2) is the steady forward speed vector in the body-fixed coordinate system defined in equation (41).ñ9 is the normal vector on the body surface.r9 = x, y, z ð Þ is a position vector of a point on the body surface.…”

Section: Formulation Of Bvp In the Body-fixed Coordinate Systemmentioning

confidence: 99%

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A numerical study of the second-order wave excitation of ship springing in infinite water depth

Shao

Faltinsen

2011

Proceedings of the Institution of Mechanical Engineers, Part M:

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Assuming the wave steepness of the incident waves and the ship motions are small, the second-order weakly-nonlinear hydrodynamic problem of a ship moving with constant forward speed is studied numerically in a consistent way. The boundary value problem is formulated in a body-fixed coordinate system and the perturbation scheme is used. This formulation does not include any derivatives of the velocity potential on the right-hand side of the body-boundary conditions, and thus avoid the difficulties associated with the terms similar to the so-called m j -terms and their derivatives. The second-order sum-frequency wave excitation of ship springing is studied in both monochromatic and bichromatic headsea waves. Different Froude numbers are considered. A time-domain Higher-Order Boundary Element Method based on cubic shape function is used as a numerical tool. An upstream finite difference scheme is used for longitudinal derivative terms in the free-surface conditions. For a modified Wigley hull in head-sea waves, it is found that the second-order velocity potential gives dominant contribution to second-order wave excitation of ship springing in the wave frequency region where sum-frequency springing occurs. Quadratic velocity terms in the Bernoulli equation have a relatively small contribution. The numerical results also demonstrate strong dependency of the second-order wave excitation of ship springing on the Froude numbers for small wave lengths. The effect of beam and draft is investigated.

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Section: Formulation Of Bvp In the Body-fixed Coordinate Systemmentioning

confidence: 99%

“…The discussion on different sources of damping effects can be found in So¨ding. 41 However, the wave excitation is the only focus of this study.…”

Section: Convergence Studiesmentioning

confidence: 99%