Harmonic Deflections of an Infinite Floating Plate

Colin Fox and Hyuck Chung


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 non-dimensional formulation
are discussed.

Floating plate, sea ice, ice dynamics, Green's function, scaling law, waves

Math Review Classification
Primary 74F10 ; Secondary 35D99, 76B15

Last Updated
July 2002

33 pages

This article is available in: