  A variational principle is proposed to derive the governing equations for the
problem of ocean wave interactions with a floating ice shelf, where the ice
shelf is modelled by the full linear equations of elasticity and has an
Archimedean draught. The variational principle is used to form a thin-plate
approximation for the ice shelf, which includes water--ice coupling at the
shelf front and extensional waves in the shelf, in contrast to the benchmark
thin-plate approximation for ocean wave interactions with an ice shelf. The
thin-plate approximation is combined with a single-mode approximation in the
water, where the vertical motion is constrained to the eigenfunction that
supports propagating waves. The new terms in the approximation are shown to
have a major impact on predictions of ice shelf strains for wave periods in the
swell regime.
