Approximate Analysis of a Viscoelastic Plate Floating on a Fluid of Finite Depth

The responses of a very large floating structure (VLFS), which is modeled as a thin viscoelastic plate floating on a fluid of finite depth, are analytically studied within the framework of the nonlinear potential flow theory. We use the Laplace equation with the dynamical boundary condition to express a balance among the hydrodynamic, inertial, and viscoelastic forces. For the case of steady-state incident waves, we obtain convergent series solutions for plate deflection and velocity potential by choosing the optimal convergence-control parameter C0 and proper auxiliary linear operators in the homotopy analysis method (HAM). The strain relaxation time for the viscoelastic plate is studied, and the result shows that the plate deflection decreases when the retardation time increases. The influences of other physical parameters on the viscoelastic plate are also discussed. The nonlinearity of dispersion relation and the retardation time of the plate have important and non-negligible effects on the responses of the VLFS. The results obtained here may be helpful in understanding the different physical parameters to model hydroelastic responses of a VLFS in the real ocean.