Second-order hydroelastic responses for flexible floating bodies are investigated by using a direct time-domain Higher Order Boundary Element Method (HOBEM) which was developed at Osaka University (He and Kashiwagi, 2014). To calculate the second-order hydrodynamic forces, the second-order velocity potential is obtained by solving the second-order boundary-value problem based on the regular perturbation method. Hydroelastic responses are calculated by using a modal superposition method with generalized modes. The modal vector of vertical bending is obtained by both beam theory and Finite Element Method (FEM). To consider nonlinear hydroelastic responses, the second-order generalized hydrodynamic forces are computed using the inner product of mode shape and normal vector of a flexible surface based on the method of Huang and Rigg (2000). For validation of the linear response, Malenica and Remy barge models are selected (Malenica et al, 2003; Remy et al, 2006), and the hydroelastic responses are compared with experimental results and other numerical results. For the second-order responses, a flexible modified Wigley model is used and the existence of second-order resonance is confirmed.


Nowadays, hydroelastic responses have become important issues for ship design due to increase in ship size. To confirm the effect of hydroelastic response on the structural strength of a ship, much investigation has been conducted on the global responses such as springing and slam-ming-induced whipping. Several types of investigation methods like direct measurement, model experiment and numerical simulation have been also performed. Among them, experiments have clearly shown that nonlinear (higher order) springing phenomena usually happen at moderate sea states (Miyake et al., 2008; Hong and Kim, 2014). On the other hand, most of numerical investigations for the nonlinear springing have been made using a linear solution up to now (Kim et al., 2009; Malenica and Derbanne, 2014). Although some numerical simulations for the nonlinear springing have been performed by computing nonlinear Froude-Krylov forces, the diffraction effect at higher order modes needs to be confirmed for a flexible body. Recently, Shao and Faltinsen (2014) calculated the second-order excitation force for two-node vibration of ship models using a body-fixed coordinate method. They showed that the second-order hydrodynamic force at forward speed is also strongly affected by the second-order velocity potential and the forward speed affects the results in a short wave region.

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