Variational Principles Related to Motions of an Elastic Floating Plate in Nonlinear Water Waves

摘要

New variational principles for the three-dimensional interaction problem between a nonlinear free surface flow and motions of an elastic plate floating on water surface are derived from Hamilton's principle. The linear theory is used for the plate. These variational principles are basis to calculate the hydroelastic responses of very large pontoon type floating structure and nonlinear transformation of surface waves in shallow water. Hamilton-kelvin's variational principle is derived from Hamilton's principle. The arguments of this variational principle are the velocity vector of water, the water elevation and the vertical displacement of the plate. Hamilton-Dirichlet's variational principle is obtained by transforming the velocity vector in Hamilton-kelvin's variational principle into the velocity potential. By assuming that the vertical distribution of velocity potential is represented by a linear combination of known functions, a variational principle is obtained. The arguments of this variational principle are the two-dimensional potential functions of the horizontal coordinate, the water elevation and the vertical displacement of the plate. From this variational principle, differential equations for the vertical displacement of the floating plate and the nonlinear wave field are obtained.