Interaction of surface water waves with a vertical elastic plate: a hypersingular integral equation approach

2016 ◽  
Vol 67 (5) ◽  
Author(s):  
Rumpa Chakraborty ◽  
Arpita Mondal ◽  
R. Gayen
Keyword(s):  
Integral Equation ◽  
Surface Water ◽  
Elastic Plate ◽  
Water Waves ◽  
Hypersingular Integral Equation ◽  
Equation Approach ◽  
Hypersingular Integral ◽  
Integral Equation Approach ◽  
Surface Water Waves ◽  
Vertical Elastic Plate

Trapping of water waves by submerged plates using hypersingular integral equations

1995 ◽  
Vol 284 ◽  
pp. 359-375 ◽  
Author(s):  
Neil F. Parsons ◽  
P. A. Martin
Keyword(s):  
Integral Equation ◽  
Surface Water ◽  
Water Waves ◽  
Velocity Potential ◽  
Finite Depth ◽  
Circular Cylinders ◽  
Hypersingular Integral Equation ◽  
Flat Plates ◽  
Hypersingular Integral ◽  
Surface Water Waves

The trapping of surface water waves by a thin plate in deep water is reduced to finding non-trivial solutions of a homogeneous, hypersingular integral equation for the discontinuity in velocity potential across the plate. The integral equation is discretized using an expansion-collocation method, involving Chebyshev polynomials of the second kind. A non-trivial solution to the problem is given by the vanishing of the determinant inherent in such a method. Results are given for inclined flat plates, and for curved plates that are symmetric with respect to a line drawn vertically through their centre. Comparisons with published results for horizontal flat plates (in water of finite depth) and for circular cylinders are made.

scholarly journals WATER WAVE SCATTERING BY A THIN VERTICAL SUBMERGED PERMEABLE PLATE

2021 ◽  
Vol 26 (2) ◽  
pp. 223-235
Author(s):  
Rupanwita Gayen ◽  
Sourav Gupta ◽  
Aloknath Chakrabarti
Keyword(s):  
Integral Equation ◽  
Water Waves ◽  
Water Wave ◽  
Wave Theory ◽  
Hypersingular Integral Equation ◽  
Cauchy Type ◽  
Hypersingular Integral ◽  
Permeable Plate ◽  
Linear Water Wave Theory ◽  
Surface Water Waves

An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov’s book [7]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock’s theorems.

Scattering of surface waves obliquely incident on a fixed half immersed circular cylinder

1984 ◽  
Vol 96 (2) ◽  
pp. 359-369 ◽  
Author(s):  
B. N. Mandal ◽  
S. K. Goswami
Keyword(s):  
Integral Equation ◽  
Surface Water ◽  
Circular Cylinder ◽  
Water Waves ◽  
Wave Number ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Obliquely Incident ◽  
Surface Water Waves

AbstractThe problem of scattering of surface water waves obliquely incident on a fixed half immersed circular cylinder is solved approximately by reducing it to the solution of an integral equation and also by the method of multipoles. For different values of the angle of incidence and the wave number the reflection and transmission coefficients obtained by both methods are evaluated numerically and represented graphically to compare the results obtained by the respective methods.

scholarly journals Scattering of water waves by a submerged thin vertical wall with a gap

1998 ◽  
Vol 39 (3) ◽  
pp. 318-331 ◽  
Author(s):  
Sudeshna Banerjea ◽  
B. N. Mandal
Keyword(s):  
Integral Equation ◽  
Surface Water ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Water Waves ◽  
Water Wave ◽  
Vertical Wall ◽  
Multiple Integral ◽  
Cauchy Kernel ◽  
Surface Water Waves

AbstractA train of surface water waves normally incident on a thin vertical wall completely submerged in deep water and having a gap, experiences reflection by the wall and transmission through the gaps above and in the wall. Using Havelock's expansion of water wave potential, two different integral equation formulations of the problem are presented. While the first formulation involves multiple integral equations which are solved here by reducing them to a singular integral equation with Cauchy kernel in a double interval, the second formulation involves a first-kind singular integral equation in a double interval with a combination of logarithmic and Cauchy kernel, the solution of which is obtained by utilizing the solution of a singular integral equation with Cauchy kernel in (0, ∞) and also in a double interval. The reflection coefficient is evaluated by both the methods.

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