The problems of radiation (sway, heave and roll) of surface and flexural-gravity waves by a submerged cylinder are investigated for two configurations, concerning; (i) a freely floating finite elastic plate modelling an ice floe, and (ii) two semi-infinite elastic plates separated by a region of open water (polynya). The fluid of finite depth is assumed to be inviscid, incompressible and homogeneous. The linear two-dimensional problems are formulated within the framework of potential-flow theory. The method of mass sources distributed along the body contour is applied. The corresponding Green's function is obtained by using matched eigenfunction expansions. The radiation load (added mass and damping coefficients) and the amplitudes of vertical displacements of the free surface and elastic plates are calculated. Reciprocity relations which demonstrate both symmetry of the radiation load coefficients and the relation of damping coefficients with the far-field form of the radiation potentials are found. It is shown that wave motion essentially depends on the position of the submerged body relative to the elastic plate edges. The results of solving the radiation problem are compared with the solution of the diffraction problem. It is noted that resonant frequencies in the radiation problem correlate with those frequencies at which the reflection coefficient in the diffraction problem has a local minimum.

The problem of unsteady behaviour of a floating thin plate is solved. The simultaneous motion of the plate and the fluid is considered within the framework of linear shallow-water theory. It is assumed that the bottom is not uniform in depth under the heterogeneous plate represented by an infinitely extended strip of finite width. The elastic deflection of the plate is expressed by a superposition of modal functions of a homogeneous beam with free edge conditions. The time-dependent unknown amplitudes are determined from the solution of a linear set of ordinary differential equations with constant coefficients. The eigenvalues of this set are determined numerically. Proposed method is used for the solution of three unsteady problems: the scattering of localized surface wave by an elastic plate, decay of the initial deformation of the plate in the fluid at rest and the action of a periodic load on a plate. Numerical calculations are performed for the ice sheet with the variable thickness and various bottom topographies.

The results of solving the linear problem of steady-state oscillations of a horizontal cylinder submerged in fluid on whose upper boundary a semi-infinite elastic plate with free edge floats are given. The remaining part of the fluid surface is free. The contour-distributed mass source method is used. The corresponding Green's function is constructed using eigenfunction expansions. The hydrodynamic load and the amplitudes of vertical displacements of the free surface and elastic plate are calculated. Equivalence relations which demonstrate both symmetry of the apparent mass and damping factors and connection of the damping factors with the wave amplitudes in the far field are derived.Keywords: linear wave theory, oscillations of a submerged cylinder, floating elastic plate, hydrodynamic load, equivalence relations.In the far field we must require to satisfy the radiation condition that means that the generated waves are divergent.

Abstract

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