Water wave interaction with an array of submerged circular plates: Hankel transform approach
Siming Zheng, Hui Liang, Simone Michele, Deborah Greaves
Abstract
A Hankel transform based model is developed to study water wave interaction with an array of thin submerged horizontal perforated and/or elastic circular plates. The integral equations are formulated in terms of unknown functions related to the jump in velocity potential across each plate. A Galerkin method is adopted to the solution of these integral equations and the velocity potential jump across the plate is expressed in terms of Fourier-Gegenbauer series. The present model is found to be valid for multiple plates distributed arbitrarily, including the staggered arrangement, for which the traditional eigenfunction matching method would not work.
Topics & Concepts
Hankel transformEigenfunctionMathematical analysisMathematicsJumpGalerkin methodFourier transformIntegral equationIntegral transformSeries (stratigraphy)Velocity potentialGeometryEigenvalues and eigenvectorsPhysicsBoundary value problemFinite element methodGeologyQuantum mechanicsThermodynamicsPaleontologyNumerical methods in engineeringWave and Wind Energy SystemsFluid Dynamics and Vibration Analysis