Misaligned wind and wave loading cause bi-directional vibrations of offshore wind turbines. In this study, a three dimensional pounding pendulum tuned mass damper (3d-PPTMD) is developed to reduce the vibration of a monopile type fixed-bottom offshore wind turbine in two directions. The proposed 3d-PPTMD is comprised of a pendulum mass-damper along with a cylindrical pounding layer where viscoelastic material is used to increase the dissipation of kinetic energy during pounding phase. A complete numerical model of the monopile fixed-bottom offshore wind turbine with the 3d-PPTMD is derived via Euler–Lagrangian equations. The wind loading is computed by the Blade Element Momentum approach, and the hydrodynamic loading is estimated via JONSWAP spectrum and Morisons equation. The effectiveness of the proposed 3d-PPTMD is examined on a monopile 5 MW baseline wind turbine subjected to misaligned wind and wave loading. The optimal design parameters of the proposed 3d-PPTMD are determined and its mitigation performance is examined under different loading scenarios and off-tuning effects. Dual linear TMDs and a regular three dimensional pendulum tuned mass damper (3d-PTMD) are employed for comparison. Results reveal that a well-designed 3d-PPTMD can effectively suppress the bi-directional vibration of the offshore wind turbine exposed to misaligned wind and wave loading. In addition, the 3d-PPTMD is more robust than the dual linear TMDs and regular 3d-PTMD to overcome the off-tuning effect. Moreover, the proposed 3d-PPTMD requires approximately $35\%$ and $25\%$ smaller space than the dual linear TMDs and the regular 3d-PTMD respectively, which is advantageous for real application.

风浪负荷不平衡会导致海上风力涡轮机的双向振动。在这项研究中，开发了三维捣摆调谐质量阻尼器（3d-PPTMD），以减少单桩式固定底海上风力发电机在两个方向上的振动。拟议的3d-PPTMD包括一个摆锤质量阻尼器以及一个圆柱状的减震层，其中使用粘弹性材料来增加减震阶段的动能耗散。通过Euler-Lagrangian方程推导了带有3d-PPTMD的单桩固定底海上风力发电机的完整数值模型。风荷载是通过叶片单元动量法计算的，而水动力荷载是通过JONSWAP谱和Morisons方程估算的。拟议的3d-PPTMD的有效性是在遭受风和波浪载荷未对准的5兆瓦单桩基准风力涡轮机上进行的。确定了建议的3d-PPTMD的最佳设计参数，并研究了其在不同载荷情况和失谐效应下的缓解性能。比较采用双线性TMD和常规三维摆调谐质量阻尼器（3d-PTMD）。结果表明，精心设计的3d-PPTMD可以有效地抑制海上风轮机在风浪荷载作用下的双向振动。此外，3d-PPTMD比双线性TMD和常规3d-PTMD更坚固，可克服失谐效应。此外，拟议的3d-PPTMD大约需要 确定了建议的3d-PPTMD的最佳设计参数，并研究了其在不同载荷情况和失谐效应下的缓解性能。比较采用双线性TMD和常规三维摆调谐质量阻尼器（3d-PTMD）。结果表明，精心设计的3d-PPTMD可以有效地抑制海上风轮机在风浪荷载作用下的双向振动。此外，3d-PPTMD比双线性TMD和常规3d-PTMD更坚固，可克服失谐效应。此外，拟议的3d-PPTMD大约需要 确定了建议的3d-PPTMD的最佳设计参数，并研究了其在不同载荷情况和失谐效应下的缓解性能。比较采用双线性TMD和常规三维摆调谐质量阻尼器（3d-PTMD）。结果表明，精心设计的3d-PPTMD可以有效地抑制海上风轮机在风浪荷载作用下的双向振动。此外，3d-PPTMD比双线性TMD和常规3d-PTMD更坚固，可克服失谐效应。此外，拟议的3d-PPTMD大约需要 比较采用双线性TMD和常规三维摆调谐质量阻尼器（3d-PTMD）。结果表明，精心设计的3d-PPTMD可以有效地抑制海上风轮机在风浪荷载作用下的双向振动。此外，3d-PPTMD比双线性TMD和常规3d-PTMD更坚固，可克服失谐效应。此外，拟议的3d-PPTMD大约需要 比较采用双线性TMD和常规三维摆调谐质量阻尼器（3d-PTMD）。结果表明，精心设计的3d-PPTMD可以有效地抑制海上风轮机在风浪荷载作用下的双向振动。此外，3d-PPTMD比双线性TMD和常规3d-PTMD更坚固，可克服失谐效应。此外，拟议的3d-PPTMD大约需要$35％$ 和 $25％$ 比双线性TMD和常规3d-PTMD的空间更小，这对于实际应用是有利的。