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Anthony N. Williams

Bio: Anthony N. Williams is an academic researcher. The author has contributed to research in topics: Integral equation & Inertia. The author has an hindex of 2, co-authored 3 publications receiving 53 citations.

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TL;DR: In this paper, two approximate methods are presented for the calculation of the wave induced forces and moments on a vertical, surface-piercing cylinder of elliptic cross section, which provide a substantial reduction in computational effort when Compared with the exact solution which involves the numerical evaluation of Mathieu functions.
Abstract: Two approximate methods are presented for the calculation of the wave induced forces and moments on a vertical, surface‐piercing cylinder of elliptic cross section. Both methods provide a substantial reduction in computational effort when Compared with the exact solution which involves the numerical evaluation of Mathieu functions. One method involves the expansion of the exact expressions for the forces and moments for small values of the elliptic eccentricity parameter. The second method is based on Green's theorem and gives rise to an integral equation for the fluid velocity potential on the cylinder surface. Numerical results are presented for a range of relevant parameters and show excellent agreement with the computed values of the exact solution.

45 citations

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TL;DR: In this paper, an approximate method is presented to investigate the hydrodynamic interactions between a pair of free-standing, bottom-mounted, flexible circular cylinders subjected to high-frequency, horizontal ground motion.
Abstract: An approximate method is presented to investigate the hydrodynamic interactions between a pair of free‐standing, bottom‐mounted, flexible circular cylinders subjected to high‐frequency, horizontal ground motion. The cylinders are aligned parallel to the direction of ground excitation and the response of each is assumed to be one‐dimensional and governed by a beam equation. The solution technique for the fluid velocity potential uses the modified plane‐wave method and involves replacing divergent radiated and scat‐ tered waves by equivalent plane waves together with nonplanar correction terms. Numerical results are presented, which illustrate the influence of the various geometrical and material properties of the cylinders on the hydrodynamic loading and associated dynamic response for several pairs of example structures. It is found that the inclusion of fluid compressibility in the formulation leads to predictions of quite significant interactions between squatty cylinders at high frequencies, even at a ...

12 citations

Journal ArticleDOI
TL;DR: In this paper, the integral equation method is utilized to calculate the wave-induced loading on a surface-piercing cylinder of circular cross-section inclined at an arbitrary angle to the sea bed.
Abstract: The integral equation method is utilized to calculate the wave-induced loading on a surface-piercing cylinder of circular cross-section inclined at an arbitrary angle to the sea bed. Numerical values of the various force and moment components are presented for a range of wave and cylinder parameters. The computed estimates of the force coefficients show good agreement in the inertial limit with published experimental results. In addition, the estimates confirm that the inertia force on an inclined cylinder may be severely underestimated by using the vectorial form of the Morison equation with a mass coefficient appropriate to the corresponding vertical cylinder case.

2 citations


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TL;DR: In this article, the authors derived a relation for the fluid motion through thin porous structures in addition to the conventional governing equation and boundary conditions for small-amplitude waves in ideal fluids.
Abstract: Diffraction of water waves by porous breakwaters is studied based on the linear potential wave theory. The formulation of the problem includes a newly derived relation for the fluid motion through thin porous structures in addition to the conventional governing equation and boundary conditions for small-amplitude waves in ideal fluids. The porous boundary condition, indirectly verified by collected experimental data, is obtained by assuming that the flow within the porous medium is governed by a convection-neglected and porous-effect-modeled Euler equation. A vertically two-dimensional problem with long-crested waves propagating in the normal direction of an infinite porous wall is first solved and the solution is compared with available experimental data. The wave diffraction by a semiinfinite porous wall is then studied by the boundary-layer method, in which the outer approximation is formulated by virtue of the reduced two-dimensional solution. It is demonstrated that neglect of the inertial effect of the porous medium leads to an overestimate of the functional performance of a porous breakwater.

280 citations

Journal ArticleDOI
TL;DR: In this article, a finite element model for the solution of Helmholtz problems at higher frequencies is described, which offers the possibility of computing many wavelengths in a single finite element.
Abstract: This paper describes a finite element model for the solution of Helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element. The approach is based on partition of unity isoparametric elements. At each finite element node the potential is expanded in a discrete series of planar waves, each propagating at a specified angle. These angles can be uniformly distributed or may be carefully chosen. They can also be the same for all nodes of the studied mesh or may vary from one node to another. The implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres. The wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced. Issues related to the integration and the conditioning are also discussed.

131 citations

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TL;DR: In this paper, a hydrodynamic experiment was conducted to examine the wave forces acting on the superstructure of coastal highway bridges to gain insight into the mechanical characteristics of wave forces caused by the combination of storm surges and huge waves.
Abstract: This paper presents a hydrodynamic experiment that examines the wave forces acting on the superstructure of coastal highway bridges to gain insight into the mechanical characteristics of the wave forces caused by the combination of storm surges and huge waves. The experiment is unique in that the specimen is a full bridge model, including its superstructure, substructure, and neighboring segments. After introducing the experimental setup and test program, this study analyzes the quasi-static and slamming components of the vertical wave force, the horizontal wave force of the superstructure in different clearances, wave heights, and wave periods. The test results are subsequently compared with two theoretical models suggested by Douglass and AASHTO guidelines to provide the experimental validation of those models. By comparing the test results and the existing models, a number of observations and discussions are produced to improve the accuracy of those theoretical models further.

74 citations

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TL;DR: In this paper, two new explicit empirical formulas were proposed to determine the original intensity factors on Neumann and Dirichlet boundary in the singular boundary method (SBM) solution of 2D and 3D potential and Helmholtz problems.
Abstract: This short communication proposes two new explicit empirical formulas to determine the original intensity factors on Neumann and Dirichlet boundary in the singular boundary method (SBM) solution of 2D and 3D potential and Helmholtz problems. Without numerical integration and subtracting and adding-back technique, the original intensity factors can be obtained directly by implementing the proposed explicit empirical formulas. The numerical investigations show that the SBM with these new explicit empirical formulas can provide the accurate solutions of several benchmark examples in comparison with the analytical, Boundary element method (BEM) and Regularized meshless method (RMM) solutions. In most cases, the present SBM with empirical formulas yields the similar numerical accuracy as the BEM and the SBM in which the original intensity factors are evaluated by the other time-consuming approaches. It is worthy of noting that the empirical formula costs far less CPU and storage requirements at the same number of boundary nodes and performs more stably than the inverse interpolation technique in the SBM.

55 citations

Journal ArticleDOI
TL;DR: In this paper, a semi-analytical solution methodology for the linear hydrodynamic diffraction induced by arrays of elliptical cylinders subjected to incident waves is presented, where the solution of the Laplace equation in elliptic coordinates for both the incident and the diffracted waves is formulated analytically in terms of the even and odd periodic and radial Mathieu functions.

43 citations