Resonant wave-induced vibrations of a ship hull girder, known as “springing”, is an important issue when addressing fatigue aging of the steel structure. To compute resonant wave-induced vibrations, fluid-structure interactions and associated structural and hydrodynamic properties need to be addressed. This paper introduces a time-domain numerical method that predicts higher-order springing taking into account forward speed. Structural dynamics were computed based on a beam element approach that considers vertical and horizontal bending as well as nonuniform torsion. Furthermore, mass and stiffness matrices accounted for strong coupling effects between hull girder bending and torsion. The hydrodynamic solver coupled the fully nonlinear stationary free surface flow with the oscillatory flow and considered geometrical nonlinearities caused by the changing wetted surface due to the incident waves, nonlinear rigid body motions and linear elastic vibrations. Numerical predictions were validated against model tests of a post-Panamax containerships at forward speed. Dry and wet natural frequencies and midship vertical bending, horizontal bending and torsional moments induced by higher order springing vibrations compared favourably to experimental measurements.

解决钢结构疲劳老化时，船体梁的共振波引起的振动（称为“弹跳”）是一个重要问题。为了计算共振波引起的振动，需要解决流固耦合以及相关的结构和流体动力学特性。本文介绍了一种时域数值方法，该方法在考虑前进速度的情况下预测高阶弹跳。基于梁单元方法计算结构动力学，该方法考虑了垂直和水平弯曲以及不均匀的扭转。此外，质量和刚度矩阵是造成船体大梁弯曲和扭转之间强烈耦合的原因。流体动力学求解器将完全非线性的静止自由表面流与振荡流耦合在一起，并考虑了由于入射波，非线性刚体运动和线性弹性振动引起的润湿表面变化而引起的几何非线性。相对于巴拿马型货船的后备船模型测试以向前的速度验证了数值预测。与实验测量相比，高阶弹性振动引起的干，湿固有频率和船中垂直弯曲，水平弯曲和扭转力矩。