Abstract
The diffraction problem of hydroelastic waves beneath an ice sheet by multiple bottom-mounted circular cylinders is considered. The elastic thin-plate theory is adopted to model the ice sheet, while the linearized velocity potential theory adopted for the fluid flow. The velocity potential corresponding to each cylinder is expanded into a series of eigenfunctions, and the total potential is expressed as a summation of these expansions over the entire NC number of cylinders. For each cylinder, the Green’s second identity is used outside its domain to obtain a set of linear equations. For each different cylinder, the domain used is different. NC cylinders give NC sets of coupled linear equations. Investigations are made for different arrangements of cylinders, piercing through ice sheets. Results for the wave forces on the cylinders with clamped and free conditions of the ice edge are obtained. Physical phenomena corresponding to cylinders arranged in square, in an array, in a double-array and in a staggered double array are discussed.
Highlights
Vertical circular columns are commonly adopted in ocean engineering as components of coastal and offshore structures, such as bridge pylons and tension leg platforms
By means of eigenfunction expansions and the Green’s second identity repeatedly for domains outside individual cylinders, solutions for interactions of hydroelastic waves with multiple vertical cylinders have been obtained in an efficient way
The wave forces on the cylinders piercing through ice sheet under clamped and free edge conditions are obtained and analysed
Summary
Vertical circular columns are commonly adopted in ocean engineering as components of coastal and offshore structures, such as bridge pylons and tension leg platforms. Extensive research has been conducted on the water wave diffraction by vertical cylinders in open water. Havelock [1] considered the diffraction problem of a single vertical circular cylinder in regular wave of infinite depth and derived an exact solution. MacCamy and Fuchs [2] used the method of separation of variables involving Hankel function for a circular cylinder in the finite water depth. For a vertical cylinder with an elliptic cross section, Chen and Mei [3] adopted the variable separation method involving Mathieu functions in the elliptic cylindrical coordinate system. Williams [4] adopted both semi-analytical and numerical methods for the diffraction problem of an elliptic cylinder. The first one was based on elliptic eccentricity, and the Mathieu functions in the
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