= Flexural-gravity wave
{title2=$\omega^2=(gk+\beta k^5)/(1+\alpha k)$}
A flexural-gravity wave bends a floating <elastic plate> while displacing the underlying water. For a uniform plate with areal mass $m$ and <bending stiffness> $D$ above inviscid deep water of <mass density> $\rho_w$, put $\alpha=m/\rho_w$ and $\beta=D/\rho_w$. Combining the plate equation with the water's <kinematic boundary condition> gives the displayed <dispersion relation>. Both <gravitational acceleration> and plate bending restore displacement; water and plate inertia resist acceleration. It assumes small amplitude, no prestress and negligible shear deformation of the plate.
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