The body-fixed coordinate system is applied to the wave-body interaction problem of a small-depth elastic structure which has both rigid and elastic body motions in head waves. In the weakly non-linear assumption, the perturbation scheme is used and the expansion is conducted up to second-order to consider several non-linear quantities. To solve the boundary value problem, linearization is carried out based not on inertial coordinate but on body-fixed coordinate which could be accelerated by a motion of a body. At first, the main feature of the application of body-fixed coordinate system for a seakeeping problem is briefly described. After that the transformation of a coordinate system is extended to consider an elastic body motion and several physical variables are re-described in the generalized mode. It has been found that the deformation gradient could be used for the transformation of a coordinate system if several conditions are satisfied. Provided there are only vertical bending in elastic modes and the structure has relatively small depth, these conditions are generally satisfied. To calculate an elastic motion of a body, the generalized mode method is adopted and the mode shape is obtained by solving eigen-value problem of dynamic beam equation. In the boundary condition of the body-fixed coordinate system, the motion effect reflected to free-surface boundary is considered by extrapolating each mode shape to the horizontal direction from a body. At last, simple numerical tests are implemented as a validation process. The second-order hydrodynamic force of a freely floating hemisphere is first calculated in zero forward speed condition. Next, motion and added resistance of a ship with forward speed are considered at different flexibility to confirm the effect of an elastic body motion in body-fixed coordinate system.

将体固定坐标系应用于迎面波中既有刚体运动又有弹性体运动的小深度弹性结构的波体相互作用问题。在弱非线性假设中，使用了微扰方案，并且将扩展进行到二阶以考虑几个非线性量。为了解决边值问题，线性化不是基于惯性坐标，而是基于可以被物体运动加速的物体固定坐标。首先简要介绍了体固定坐标系在耐波性问题中的应用的主要特点。之后，坐标系的变换被扩展到考虑弹性体运动，并且在广义模式中重新描述了几个物理变量。已经发现，如果满足几个条件，变形梯度可以用于坐标系的变换。如果弹性模态中只有竖向弯曲，结构深度较小，一般都满足这些条件。为了计算物体的弹性运动，采用广义振型法，通过求解动力梁方程的特征值问题得到振型。在物体固定坐标系的边界条件下，通过从物体向水平方向外推每个模态，考虑反射到自由表面边界的运动效应。最后，简单的数值测试被实施为验证过程。首先在零前进速度条件下计算自由浮动半球的二阶水动力。