# Three-dimensional finite element analysis of the diffraction-radiation problem of hydrodynamically compact structures

TL;DR: The finite element method for solving the linear floating body hydrodynamic problem is considered with a hierarchy of boundary damper options for modelling the far field as discussed by the authors, which is validated using two simple examples for which added mass and damping coefficients are computed over a wide range of frequencies.

About: This article is published in Marine Structures.The article was published on 1995-01-01. It has received 3 citations till now. The article focuses on the topics: Finite element method & Added mass.

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University of Plymouth

^{1}, Tsinghua University^{2}, Kyushu University^{3}, University College Cork^{4}TL;DR: In this paper, a semi-analytic model based on linear potential theory is developed to solve wave radiation from an array of truncated cylinders with arbitrary cross sections, free to oscillate independently in water of finite depth.

10 citations

### Cites background from "Three-dimensional finite element an..."

...Therefore, solving the problem of wave radiation 24 from offshore structures has been a subject of considerable research interest (Bai and Eatock Taylor, 25 2006; Krishnankutty and Vendhan, 1995; Newman, 2005; Sheng et al., 2015; Taghipour et al., 2008)....

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TL;DR: In this paper, two new elliptic dampers are proposed, one for beam-on incidence and the other for general wave incidence, and the performance of all the three dampers is studied using a numerical example of diffraction by an elliptic cylinder.

Abstract: In a domain method of solution of exterior scalar wave equation, the radiation condition needs to be imposed on a truncation boundary of the modelling domain. The Bayliss, Gunzberger and Turkel (BGT) boundary dampers of first- and second-orders, which require a circular cylindrical truncation boundary in the diffraction-radiation problem of water waves, have been particularly successful in this task. However, for an elongated body, an elliptic cylindrical truncation boundary has the potential to reduce the modelling domain and hence the computational effort. Grote and Keller proposed extension of the first- and second-order BGT dampers for the elliptic radiation boundary and used these conditions to the acoustic scattering by an elliptic scatterer using the finite difference method. In this paper, these conditions are implemented for the problem of diffraction of water waves using the finite element method. The proposed extension works well only for head-on wave incidence. To remedy this, two new elliptic dampers are proposed, one for beam-on incidence and the other for general wave incidence. The performance of all the three dampers is studied using a numerical example of diffraction by an elliptic cylinder

6 citations

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TL;DR: In this paper, the authors presented an experimental cum analytical investigation on lateral sloshing behavior under simulated vibrating conditions on a fixed base rectangular container with water, which was designed to suit experimental requirements and the walls were made of Perspex sheets in order to view the slohing phenomena and for image capturing purposes.

Abstract: Sloshing is one of the major concerns for liquid storage tanks and the vibration characteristics of the contained liquid require lot of research attention. Simulated experimental investigations using triaxial shake tables are rare in this field and the non linear dynamic behavior of the structure is of interest, be it during transportation of liquids or during earthquakes. The paper presents an experimental cum analytical investigation on lateral sloshing behavior under simulated vibrating conditions on a fixed base rectangular container with water. The tank has been designed to suit experimental requirements and the walls were made of Perspex sheets in order to view the sloshing phenomena and for image capturing purposes. The behavior of the system is identified during dynamic loading under lateral sweep sine excitation and simulated random vibration studies were carried out further on the 3D shaking table. Sloshing natural frequencies, wave amplitudes and dynamic pressures on the tank walls are measured...

4 citations

### Cites methods from "Three-dimensional finite element an..."

...Finite element method for solving the linear floating body hydrodynamic problem is considered by researchers with a hierarchy of boundary damper options for modelling the far field (Krishnankutty and Vendhan, 1995)....

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##### References

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01 Jan 1983

TL;DR: In this article, the authors present selected theoretical topics on ocean wave dynamics, including basic principles and applications in coastal and offshore engineering, all from a deterministic point of view, and the bulk of the material deals with the linearized theory.

Abstract: The aim of this book is to present selected theoretical topics on ocean wave dynamics, including basic principles and applications in coastal and offshore engineering, all from the deterministic point of view. The bulk of the material deals with the linearized theory.

2,003 citations

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TL;DR: The method utilizes a source density distribution on the surface of the body and solves for the distribution necessary to make the normal velocity zero on the boundary and the flow velocities at points both on and off the body surface are calculated.

Abstract: : A method is described for calculating, with the aid of an electronic computer, the incompressible potential flow about arbitrary, non-lifting, three- dimensional bodies. The method utilizes a source density distribution on the surface of the body and solves for the distribution necessary to make the normal velocity zero on the boundary. Plane quadrilateral surface elements are used to approximate the body surface, and the integral equation for the surface source density is replaced by a set of linear algebraic equations for the values of the source density on each of the quadrilateral elements. After this set of equations has been solved, which is accomplished by a Seidel iterative procedure, the flow velocities at points both on and off the body surface are calculated. This approach is completely general. Bodies are not required to be slender, analytically defined, or simply connected.

370 citations

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TL;DR: In this paper, the added mass and damping coefficients associated with the periodic motions of a floating hemisphere are derived for two physically distinct cases of heave and surge, where these nautical terms refer respectively to a vertical or horizontal oscillation of the body.

Abstract: The object of this paper is to derive the added mass and damping coefficients associated with the periodic motions of a floating hemisphere. Two physically distinct cases are considered; namely those of heave and surge, where these nautical terms refer respectively to a vertical or horizontal oscillation of the body. Computations have been done and the values found for the various force coefficients are presented in tabulated form. A brief derivation of the long- and short-wave asymptotics of these coefficients has also been included.

241 citations

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TL;DR: In this paper, the authors consider the case of a ship lying dead in the water and assume that the body does not disturb the water much during its forward motion, for example, slenderness or thinness.

Abstract: We shall restrict ourselves here to floating bodies without any means of propelling themselves. The body may, of course, be a ship lying dead in the water, but there is no real limitation to practical shapes of any particular sort except that we shall suppose the body to be hydrostatically stable. This will restrict the extent of this survey in an important way: we are able to slough off all effects associated with an average velocity of the body. Since mathematical solution of problems almost inevitably proceeds by way of linearization of the boundary conditions, this means that we may avoid introducing a linearization parameter whose smallness expresses the fact that the body doesn't disturb the water much during its forward motion, for example, slenderness or thinness. If we do introduce such a geometrical assumption, it will be an additional approximation, not one forced upon us by the physical situation. Fortunately, Newman's (1970) article treats, among other things, the recent advances in the theory of motion of slender ships under way. More can be found in a paper by Ogilvie (1964) . We shall assume from the beginning that motions are small and take this into account in formulating equations and boundary conditions. Further more, we shaH assume the fluid inviscid, and without surface tension. It is not difficult to write down equations and boundary conditions for a less restricted problem. However, since most results are for the case of small motions and since the perturbation expansions associated with the deriva tion of the linearized problem from the more exact one do not present any special points of interest, it seems more efficient to start with the simpler problem. Even so, some account will be given of recent attempts to consider nonlinear problems.

165 citations