Second order nonlinear hydroelastic analysis of floating bodies - Theory

By integrating the second-order fluid pressure over the instantaneous wetted surface, the generalized first-and second-order fluid forces needed in nonlinear hydroelastic analysis were obtained. The generalized first order wave exciting forces, radiation forces and restoring forces have the same form as in linear hydroelasticity theory. One added first-order term represents the influence of the rigid body rotations on the first-order forces in the nonlinear analysis. The generalized second-order fluid forces consist of five parts: generalized second-order wave exciting forces which are related to incident and diffracted wave potentials; generalized second-order radiation forces related to radiation potentials; generalized second-order forces induced by the coupling between radiation were potentials and incident-diffracted wave potentials; generalized second-order forces induced by the movement of wetted surface; and generalized second-order forces induced by the instantaneous variation of the wetted surface. The expressions for coefficients of the generalized first-and second-order hydrodynamic forces in irregular waves were also given. Based on these, the nonlinear hydroelasticity equations for arbitrary floating bodies in irregular waves were presented, and the solution method was discussed. Numerical results of the second-order nonlinear hydroelastic analysis of ocean floating systems will be given in the accompanying paper.