The two-dimensional, nonlinear hydroelasticity of a mat-type VLFS is studied within the scope of linear beam theory for the structure and the nonlinear, Level I Green-Naghdi (GN) theory for the fluid. The beam equation and the GN equations are coupled through the kinematic and dynamic boundary conditions to obtain a new set of modified GN equations. These equations model long-wave motion beneath an elastic plate. A set of jump conditions that are necessary for the continuity (or the matching) of the solutions in the open water region and that under the structure is newly derived through the use of the postulated conservation laws of mass, momentum and mechanical energy. The resulting governing equations, subjected to the boundary and jump conditions, are solved by the finite-difference method in the time domain. The present model is applicable, for example, to the study of the hydroelastic response of a mat-type VLFS under the action of a solitary wave, or a frontal tsunami wave. Good agreement is observed between the present results and other published theoretical and numerical predictions, as well as experimental data. The nonlinear results show that consideration of nonlinearity is important for accurate predictions of the bending moment of the floating elastic plate. It is also found that the rigidity of the structure also greatly affects the bending moment and displacement of the structure in this nonlinear theory.
An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation
