Second-order hydroelastic responses for flexible floating bodies are investigated by using a direct time-domain Higher Order Boundary Ele-ment 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 sec-ond-order boundary-value problem based on the regular perturbation method. Hydroelastic responses are calculated by using a modal super-position 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 ex-perimental results and other numerical results. For the second-order re-sponses, a flexible modified Wigley model is used and the existence of second-order resonance is confirmed.
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机译：使用大阪大学开发的直接时域高阶边界元法（HOBEM）研究了柔性浮体的二阶水弹性响应（He and Kashiwagi，2014）。为了计算二阶水动力，通过基于规则摄动法求解二阶边值问题来获得二阶速度势。水弹性响应是通过使用具有广义模态的模态叠加方法来计算的。竖向弯曲的模态矢量通过梁理论和有限元方法（FEM）获得。为了考虑非线性流体弹性响应，根据黄和里格（2000）的方法，使用模态形状和柔性表面的法向矢量的内积来计算二阶广义流体动力。为了验证线性响应，选择了Malenica和Remy驳船模型（Malenica等，2003; Remy等，2006），并将水弹性响应与实验结果和其他数值结果进行了比较。对于二阶响应，使用了灵活的改进的Wigley模型，并确认了二阶共振的存在。
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