(untitled) (Advances in Applied Mathematics and Mechanics, 2020)
Analytical study on nonlinear hydroelastic waves beneath a very large floating structure or a thin ice sheet floating on deep water is presented. Adopting the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis to describe the floating sheet, we use the potential flow theory with the dynamic boundary condition expressing a balance among the hydrodynamic, surface tension, inertial, and elastic forces. For the case of incident progressive waves, the influences of different physical parameters on the hydroelastic waves are discussed with the aid of the homotopy analysis method. We compare the hydroelastic wave deflections based on nonlinear Plotnikov and Toland's model with those obtained by the corresponding linear Euler-Bernoulli model. It is found that the behaviors of both models are almost the same for small amplitudes, while the nonlinear plate deflections increase greatly at large amplitudes. Further, the graphical comparisons are presented to show the behavior of the angular frequency versus wave amplitudes.