WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7150
Browse
2 results
Search Results
Article Linear Wave Interaction by Multiple Vertical Cylinders of Non-Circular Smooth Cross-Section: an Iterative-Asymptotic Approach(Elsevier Ltd, 2024) Yılmaz, Oğuz; Yilmaz,O.; 01. Izmir Institute of Technology; 04.02. Department of Mathematics; 04. Faculty of ScienceThe three-dimensional problem of water wave diffraction by multiple cylinders of non-circular smooth cross-sections is studied. The rigid cylinders extend from the sea bottom to the free surface in water of finite depth. The flow is described by the linear theory of potential flow. A fourth-order asymptotic solution of the diffraction problem by a single cylinder with the asymptotic parameter being the closeness of the cross-section to a circle is combined with an iterative method to consider the effect of the wave interaction between the cylinders. The original problem for non-circular cylinders is reduced to a set of diffraction and radiation problems for circular cylinders at each asymptotic order. The velocity potentials are given by their Fourier series, and the problem solving is simplified to the algebraic operations involving the Fourier coefficients of the potentials and the shape function, which describes the cross-sectional shape of the vertical cylinder. The hydrodynamic forces and wave run-up values for geometries of two elliptical and four nearly square cylinders are presented for a range of incident wave frequencies and angles of attack. The method is validated by comparing the present hydrodynamic force results with the ones in the literature, and good agreement is reported. © 2024 Elsevier LtdArticle Citation - WoS: 7Citation - Scopus: 8Diffraction of Flexural-Gravity Waves by a Vertical Cylinder of Non-Circular Cross Section(Elsevier Ltd., 2020) Dişibüyük, Nazile Buğurcan; Yılmaz, Oğuz; Yılmaz, Oğuz; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyThe linear three-dimensional problem of flexural-gravity wave (hydro-elastic wave) diffraction by a vertical cylinder of an arbitrary smooth cross section is studied using an asymptotic approach combined with the vertical mode method for water of finite depth. The surface of the water is covered by an infinite, continuous elastic ice plate. The rigid cylinder extends from the sea bottom to the ice surface. The ice plate is frozen to the cylinder. The ice deflection is described by the equation of a thin elastic plate of constant thickness with clamped edge conditions at the cylinder. The flow under the ice is described by the linear theory of potential flows. The coupled problem of wave diffraction is solved in two steps. First, the problem is solved without evanescent waves similar to the problem of water waves diffracted by a vertical cylinder. This solution does not satisfy the edge conditions. Second, a radiation problem with a prescribed motion of the ice plate edge is solved by the vertical mode method. The sum of these two solutions solve the original problem. Both solutions are obtained by an asymptotic method with a small parameter quantifying a small deviation of the cylinder cross section from a circular one. Third-order asymptotic solutions are obtained by solving a set of two-dimensional boundary problems for Helmholtz equations in the exterior of a circle. Strains along the edge, where the ice plate is frozen to the cylinder, are investigated for nearly square and elliptic cross sections of the vertical cylinders depending on the characteristics of ice and incident wave. The strains are shown to be highest in the places of high curvatures of the cross sections. The derived asymptotic formulae can be used in design of vertical columns in ice. They directly relate the strains in ice plate to the shape of the column. © 2020 Elsevier Ltd