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During the winter months the sea around the coast of
Antarctica freezes and form a vast area of ice
covered region. The ice sheets found in this area are
large and apparently featureless. Therefore a
large-scale sea ice sheet has been modeled as a thin
elastic plate for small deflection. Partial
differential equations are derived to describe
vertical deflection of a thin elastic plate coupled
with incompressible fluid. The Fourier transform is
used to derive the vertical deflection of the ice
sheet. A fundamental solution can be expressed by
infinite summations of fractional functions at
complex roots of the dispersion equation. The
Fundamental solution is reduced to a sum of special
functions at three roots of a fifth order polynomial
when the water depth is infinite. The reflection and
transmission of wave energy between two semi-infinite
ice sheets joined by a straight-line transition is
considered. Analytical formulas for the modal
expansion of the waves in the ice sheet are derived
using the Wiener-Hopf technique. This monograph
should be a good introduction for post-graduate
students to the linear hydro-elasticity.
Antarctica freezes and form a vast area of ice
covered region. The ice sheets found in this area are
large and apparently featureless. Therefore a
large-scale sea ice sheet has been modeled as a thin
elastic plate for small deflection. Partial
differential equations are derived to describe
vertical deflection of a thin elastic plate coupled
with incompressible fluid. The Fourier transform is
used to derive the vertical deflection of the ice
sheet. A fundamental solution can be expressed by
infinite summations of fractional functions at
complex roots of the dispersion equation. The
Fundamental solution is reduced to a sum of special
functions at three roots of a fifth order polynomial
when the water depth is infinite. The reflection and
transmission of wave energy between two semi-infinite
ice sheets joined by a straight-line transition is
considered. Analytical formulas for the modal
expansion of the waves in the ice sheet are derived
using the Wiener-Hopf technique. This monograph
should be a good introduction for post-graduate
students to the linear hydro-elasticity.