Second-order hydrodynamic effects on an arrangement of two concentric truncated vertical cylinders

Mavrakos, Spyros A.; Chatjigeorgiou, Ioannis K.

doi:10.1016/j.marstruc.2008.12.003

Cited by 23 publications

(19 citation statements)

References 35 publications

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“…then G nl (R; ρ) coincides exactly with the one-dimensional Green's function that was derived by Chau and Eatock Taylor [8], and Huang and Eatock Taylor [10] (see also [12,13]). In fact, by inserting (71) into the solution of Helmholtz equation (see (27)) and performing the necessary mathematical manipulations to derive the "locked" wave component, we obtain exactly the solution for φ D 2 that was reported by Huang and Eatock Taylor [10].…”

Section: Reduction Of Green's Function In Polar Coordinatessupporting

confidence: 72%

“…An appropriate form for the diffraction potential φ D 2 that satisfies the boundary conditions on the bottom and the free surface (see Eqs. [4][5] is [9][10][11][12][13]:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…The solution was achieved by solving the associated Sturm-Liouville problem. The same procedure was followed by Mavrakos and Chatjigeorgiou [12,13] to obtain Green's function for annular domains. It should be acknowledged that, for bodies of revolution different than circular cylinders, the procedure is much more complicated.…”

Section: Introductionmentioning

confidence: 99%

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The analytic form of Green’s function in elliptic coordinates

Chatjigeorgiou

Mavrakos

2011

J Eng Math

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The purpose of this study is the derivation of a closed-form formula for Green's function in elliptic coordinates that could be used for achieving an analytic solution for the second-order diffraction problem by elliptical cylinders subjected to monochromatic incident waves. In fact, Green's function represents the solution of the so-called locked wave component of the second-order velocity potential. The mathematical analysis starts with a proper analytic formulation of the second-order diffraction potential that results in the inhomogeneous Helmholtz equation. The associated boundary-value problem is treated by applying Green's theorem to obtain a closed-form solution for Green's function. Green's function is initially expressed in polar coordinates while its final elliptic form is produced through the proper employment of addition theorems.

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Section: Reduction Of Green's Function In Polar Coordinatessupporting

confidence: 72%

“…An appropriate form for the diffraction potential φ D 2 that satisfies the boundary conditions on the bottom and the free surface (see Eqs. [4][5] is [9][10][11][12][13]:…”

Section: Mathematical Formulationmentioning

confidence: 99%

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The analytic form of Green’s function in elliptic coordinates

Chatjigeorgiou

Mavrakos

2011

J Eng Math

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“…Wu et al [16] explored the diffraction and radiation problem for a cylinder over a caisson in water of finite depth and presented the calculated results of hydrodynamic coefficients, wave forces and hydrodynamic effect of the caisson on the hydrodynamics of the cylinder. In order to achieve findings close to the experiment results, a second-order diffraction problem for truncated cylinder in finite depth water was investigated by Huang and Eatock Taylor [17] and Mavrakos and Chatjigeorgiou [18] and diffraction forces due to second-order potential was calculated. In this paper, we have considered the diffraction problem of a floating vertical circular cylinder.…”

Section: Introductionmentioning

confidence: 79%

“…The scattered wave potential in the exterior region must satisfy (18), (19), (20), (21) and (22). Therefore using the separation of variables method, as before, we have: …”

Section: Potential In the Exterior Regionmentioning

confidence: 99%

Determination of the Heave and Pitch Motions of a Floating Cylinder by Analytical Solution of its Diffraction Problem and Examination of the Effects of Geometric Parameters on its Dynamics in Regular Waves

Ghadimi

Bandari

Rostami

2012

International Journal of Applied Mathematical Research

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In this paper, diffraction problem of a floating vertical circular cylinder is studied. Detailed analytical solution for the boundary value problem to evaluate the wave loads for the cylinder with heave and pitch motions in water of finite depth in the presence of an incident wave, has been presented. Accordingly, diffraction problem for a truncated vertical circular cylinder of radius in water of finite depth has been considered. Incident wave used in this problem, is assumed to be linear with amplitude . In order to calculate the added mass and damping coefficients of the pitch motion of the body, strip theory is applied. For the heave motion, the hydrodynamic coefficients are found by the submerged disk method. Parametric studies of the effects of the wave excitation force on the floating cylinder have been performed for two different cases: 1) constant draft of the cylinder with varying water depth and 2) varying draft of the cylinder with constant water depth.

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Framework for reconstructing wave loads on a floating cylinder using monitored data of structural motion and wave elevation

Liu

Guo

2021

Journal of Fluids and Structures

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Second-order hydrodynamic effects on an arrangement of two concentric truncated vertical cylinders

Cited by 23 publications

References 35 publications

The analytic form of Green’s function in elliptic coordinates

The analytic form of Green’s function in elliptic coordinates

Determination of the Heave and Pitch Motions of a Floating Cylinder by Analytical Solution of its Diffraction Problem and Examination of the Effects of Geometric Parameters on its Dynamics in Regular Waves

Framework for reconstructing wave loads on a floating cylinder using monitored data of structural motion and wave elevation

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