Radiation of water waves by a submerged nearly circular plate

Farina, Leandro; Gama, Rômulo Lima da; Korotov, Sergey; Ziebell, Juliana Sartori

doi:10.1016/j.cam.2016.04.009

Cited by 9 publications

(9 citation statements)

References 18 publications

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“…Comparison of the magnitudes of (a): added mass, (b): damping coefficient between the results of Farina et. al 20 and our results with

d / a = 0.09

D / a^{4}

4=0,

ε / a = 0

F (r, θ) = 0

…”

Section: Numerical Results and Discussionsupporting

confidence: 81%

“…The body is considered to be a flat nearly circular plate corresponding to

κ false(ζ false) = ζ + 0.45 false(e^{ζ^{3}} - 1 false)

submerged below the free surface. The results available in Farina et al 20 . have been depicted with triangles.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The body is considered to be a flat nearly circular plate corresponding to 𝜅(𝜁) = 𝜁 + 0.45(𝑒 𝜁 3 − 1) submerged below the free surface. The results available in Farina et al 20 have been depicted with triangles. The coincidence of the triangles with the corresponding curve provides a check on the validity of the results presented here.…”

Section: Validation Of Numerical Resultsmentioning

confidence: 99%

“…Hence, we can conclude that any line segment in a small neighborhood of 𝒛 𝟎 with one end point at 𝒛 𝟎 is contracted or expanded in the ratio |𝑈 ′ (𝒛 𝟎 )|, that is, the linear change of scale at 𝒛 𝟎 due to this transformation is independent of the direction. Thus, given a length-scale 𝑎 in Ω, we can invert (20) as…”

Section: Transformation Of Plate Geometrymentioning

confidence: 99%

“…We employ the expansion–collocation method as described by Farina and Martin 16 . To tackle the weaker singularity we have used the Korobov–Conroy number theoretic method during the computations of the integrals as proposed by Farina et al 20 . In cylindrical polar coordinates

ξ = ρ \cos σ

and

η = ρ \sin σ

and the disc is given as

C = [(ρ, σ, z) : 0 \leq ρ < 1, - π \leq σ < π, z = d] .

Let,

false(ξ_{0}, η_{0} false) = false(s \cos α, s \sin α false)

, then

\tilde{S} = {(ρ^{2} + s^{2} - 2 ρ s \cos false(σ - α false))}^{1 / 2} .

Therefore, Equation () can be written as

\frac{1}{4 π} \int_{C} \tilde{g} false(ρ, σ false) [0true \frac{1}{{\tilde{S}}^{3}} + L_{0} (ρ, σ, s, α)] ρ d ρ d σ = \tilde{f} false(s, α false), false(s, α false) \in C .

…”

Section: Solution Of the Integral Equationmentioning

confidence: 99%

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Radiation of waves by a submerged nearly circular rough plate in ice‐covered ocean

Das

2021

Stud Appl Math

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A rough nearly circular (and/or circular) plate submerged in some ice‐covered ocean is undergoing a heaving motion. This radiation problem is reduced to a hypersingular integral equation over the surface of the rough plate. Perturbation method further simplifies the governing equation to get a system of hypersingular integral equations. The geometry of nearly circular plate has been conformally mapped onto a unit disc and the modified equations have been solved by a spectral method proved to be efficient for the case of a circular disc. Both rough disc and rough nearly circular plate have been considered for the numerical results. The effects of the flexural rigidity of ice cover and submergence depth of the plate on added mass and damping coefficient have been investigated along with the effect of roughness of the plate on these hydrodynamic coefficients.

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“…Comparison of the magnitudes of (a): added mass, (b): damping coefficient between the results of Farina et. al 20 and our results with