Harmonic De fl ections of an In fi nite Floating Plate

As a model for a homogeneous sheet of floating sea-ice undergoing periodic vertical loading, we treat the case of an infinite thin plate floating on a fluid of constant depth. We derive the vertical deflection of the floating plate resulting from harmonic forcing at a point and along a line. These correspond to the Green’s functions for forcing of a floating plate and floating beam, respectively. For finite water depths the solutions are written as series which are readily summable. When the fluid depth is large, or infinite, the solutions simplify to a sum of special functions, summed over three roots of a fifth-order polynomial. A non-dimensional formulation is given that reduces the results to a few canonical solutions corresponding to distinct physical regimes. Properties of the nondimensional formulation are discussed.

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