Ship rudders, as well as other common underwater appendages, take the form of hydrofoils with a finite trailing-edge thickness to produce wake vortex shedding, which causes vibrations, due to the fluid-structure interactions. Notably, underdetermined phenomena, such as the lock-in phenomenon, raise significant concerns about the structural stability of rudders of large container ships. However, methods to accurately evaluate the stability at the lock-in region are unavailable, because of its high instability, which requires high computational costs, especially for underwater applications. In this study, to address these deficiencies, methods to estimate ship rudders’ structural response and stability at lock-in regions were developed by incorporating hybrid-coupling techniques. The effect of the lock-in phenomenon was investigated using an S-N curve and the fatigue structural-failure probability to quantify the risks. The structural response to the stability analysis was obtained using hybrid-coupling fluid-structure interaction analysis methods by preconditioning the solutions to reduce the numerical instability for first bending and twisting modes with the modified Theodorsen function and to share a single interface between the structure and flow solvers on the OpenFOAM computational fluid dynamics (CFD) toolbox. The accuracy of the structural responses was validated with experiments for the lock-in frequencies, velocity range, and, most importantly, amplitudes of the structural responses of a cantilever hydrofoil. Structural-stability analysis results using the proposed methods demonstrated a significant increase in the probability of premature structural failure, thereby demonstrating the usability of the methods by structural designers in the early design stages.

船舵以及其他常见的水下附属装置采用具有有限后缘厚度的水翼形式，以产生尾涡脱落，由于流固耦合而导致振动。值得注意的是，未确定的现象，例如锁定现象，引起了对大型集装箱船舵结构稳定性的重大担忧。然而，由于锁定区域的不稳定性高，需要高计算成本，特别是对于水下应用，因此无法准确评估锁定区域的稳定性。在这项研究中，为了解决这些缺陷，通过结合混合耦合技术开发了估计锁定区域船舶舵结构响应和稳定性的方法。使用 SN 曲线和疲劳结构失效概率来量化风险，研究了锁定现象的影响。稳定性分析的结构响应是使用混合耦合流固耦合分析方法获得的，通过对解进行预处理以减少具有修改的 Theodorsen 函数的第一弯曲和扭曲模式的数值不稳定性，并在结构和流动之间共享单一界面OpenFOAM 计算流体动力学 (CFD) 工具箱上的求解器。结构响应的准确性通过锁定频率、速度范围以及最重要的悬臂水翼结构响应振幅的实验得到验证。