The present study investigates the hydroelastic response of a floating ice plate clamped to a vertical wall and subjected to an oscillatory point pressure, with particular emphasis on the effects of second-order nonlinearity on bending stresses in ice. A nonlinear potential flow model is coupled with a nonlinear thin-plate theory to systematically investigate the role of second-order nonlinearities in wave–ice interactions. It is shown that nonlinear contributions from the plate equation are negligible at second order, allowing for a linearised structural model without loss of accuracy. In contrast, nonlinear fluid–structure interactions significantly influence the strain response, particularly for loading frequencies close to resonant frequency. At these frequencies, the nonlinear self-interaction of the primary wave mode excites freely propagating second harmonics, resulting in secular growth of the second-order solution. Through a regular perturbation analysis, we derive second-order corrections to the ice deflection and show that the nonlinearity leads to localised amplification of curvature and hence strain, especially near the forcing location. Numerical results further show that for loading frequencies close to the resonant frequency, the strain distribution attains its maximum amplitude at the location of the applied load, substantially exceeding the corresponding strain levels near the clamped edge of the ice. At moderate frequencies, wave reflections from the wall cause the strain to localise near the boundary in an oscillatory pattern, with linear theory remaining accurate. However, second-order corrections may still amplify or shift strain peaks away from the wall, influencing potential fracture zones. The results demonstrate that classical linear models may severely underestimate local stress concentrations. The study underscores the importance of incorporating second-order nonlinearities and boundary effects to accurately predict strain localisation, energy transfer and potential failure zones in ice-covered waters subjected to dynamic loading.
Singh et al. (Tue,) studied this question.