Abstract
The interaction between a solitary wave and a two-dimensional floating elastic plate is studied in this paper. The modified Boussinesq equations that represent long waves beneath a floating elastic plate are derived. These equations do not take the mass of the plate into account because of the long wave assumption. Applying the matched asymptotic expansion method, conditions for a connection between the solution of the ordinary Boussinesq equations that represent long water waves and the modified Boussinesq equations are obtained. These sets of equations are solved by the finite-difference method. Numerical results demonstrate that the higher-order terms are important for the prediction of the wave celerity of a solitary wave traveling beneath a floating elastic plate. They also play an important role in the prediction of the bending moment of the floating elastic plate. The rigidity of the floating elastic plate greatly affects the bending moment due to the solitary wave. A floating elastic plate whose rigidity is low leads to a weak bending moment and vice versa.
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