Floating Membrane Breakwater

1996 ◽  
Vol 118 (1) ◽  
pp. 46-52 ◽  
Author(s):  
A. N. Williams
Keyword(s):  
Wave Reflection ◽  
Structural Parameters ◽  
Unit Length ◽  
Fluid Motion ◽  
Integral Equation Method ◽  
Equation Of Motion ◽  
Boundary Integral ◽  
Mooring Line ◽  
Hydrodynamic Properties ◽  
One Dimensional

The hydrodynamic properties of a flexible floating breakwater consisting of a membrane structure attached to a small float restrained by moorings are investigated theoretically. The tension in the membrane is achieved by hanging a clump weight from its lower end. The fluid motion is idealized as linearized, two-dimensional potential flow and the equation of motion of the breakwater is taken to be that of a one-dimensional membrane of uniform mass per unit length subjected to a constant axial force. The boundary integral equation method is applied to the fluid domain, and the dynamic behavior of the breakwater is also described through an appropriate Green function. Numerical results are presented which illustrate the effects of the various wave and structural parameters on the efficiency of the breakwater as a barrier to wave action. It is found that the wave reflection properties of the structure depend strongly on the membrane length, the magnitude of the clump weight, and the mooring line stiffness, while the membrane weight and excess buoyancy of the system are of lesser importance.

A Submerged Compliant Breakwater

1992 ◽  
Vol 114 (2) ◽  
pp. 83-90 ◽  
Author(s):  
A. N. Williams ◽  
P. T. Geiger ◽  
W. G. McDougal
Keyword(s):  
Flexural Rigidity ◽  
Numerical Technique ◽  
Structural Parameters ◽  
Unit Length ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Numerical Results ◽  
Small Scale

A numerical technique is utilized to investigate the dynamics of a submerged compliant breakwater consisting of a flexible, beamlike structure anchored to the seabed and kept under tension by a small buoyancy chamber at the tip. The fluid motion is idealized as linearized, two-dimensional potential flow and the equation of motion of the breakwater is taken to be that of a one-dimensional beam of uniform flexural rigidity and mass per unit length subjected to a constant axial force. The boundary integral equation method is applied to the fluid domain, modifications are made to the basic formulation to account for the zero thickness of the idealized structure and the singularity in the fluid velocity which occurs at the breakwater tip. The dynamic behavior of the breakwater is described through an appropriate Green function. Numerical results are presented which illustrate the global influence of the tip singularity on the solution and the effects of the various wave and structural parameters on the efficiency of the breakwater as a barrier to wave action. Small-scale physical model tests were also carried out to validate the foregoing theory. In general, the agreement between experimental and numerical results was reasonable, but with considerable scatter.

The inverse elastic scattering by an impenetrable obstacle and a crack

2020 ◽  
Author(s):  
Jianli Xiang ◽  
Guozheng Yan
Keyword(s):  
Mixed Type ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Operator ◽  
Integral Equation Method ◽  
Factorization Method ◽  
Boundary Integral ◽  
Far Field ◽  
Direct Scattering ◽  
Time Harmonic

Abstract This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by a mixed-type scatterer, which is given as the union of an impenetrable obstacle and a crack. We develop the modified factorization method to determine the shape of the mixed-type scatterer from the far field data. However, the factorization of the far field operator $F$ is related to the boundary integral matrix operator $A$, which is obtained in the study of the direct scattering problem. So, in the first part, we show the well posedness of the direct scattering problem by the boundary integral equation method. Some numerical examples are presented at the end of the paper to demonstrate the feasibility and effectiveness of the inverse algorithm.

scholarly journals The Numerical Analysis of the Flow on the Smooth and Nonsmooth Boundaries by IBEM/DBIEM

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Gang Xu ◽  
Guangwei Zhao ◽  
Jing Chen ◽  
Shuqi Wang ◽  
Weichao Shi
Keyword(s):  
Boundary Value ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Tangential Velocity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Surface Shape ◽  
Normal Vector ◽  
Computational Domain ◽  
Nonsmooth Boundary

The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.

scholarly journals Existence and uniqueness in the theory of bending of elastic plates

1986 ◽  
Vol 29 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Neumann Problems ◽  
Image Position

Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

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