An Analytical Natural Frequency Solution of Monopile Offshore Wind Turbine Considering Pile-soil Interaction
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摘要: 海上风机结构系统频率是海上风机结构和基础设计考虑的关键因素之一，桩-土相互作用对海上风机结构系统频率影响显著。基于欧拉-伯努利梁理论和传递矩阵方法，考虑水-桩-土相互作用及塔筒变截面特性，建立单桩式海上风机结构系统横向振动自振频率特征方程；将桩-水相互作用等效为附加质量、桩-土相互作用等效为线性弹簧，变截面塔筒等效为多段均匀梁，利用MATLAB中fsolve函数求解固有频率。通过与有限元分析结果进行对比，验证本文方法精度与有效性，并将本文方法应用于实际工程中，研究桩基础埋深、上部质量、转动惯量和桩-水相互作用对单桩式海上风机结构系统自振频率的影响。Abstract: The frequency of offshore wind turbine system is one of the pivotal factors that needs to be considered during the design of the structure and foundation. Based on the Euler-Bernoulli beam theory and transfer matrix method, the characteristic equation of natural vibration frequency are established by considering the water-pile-soil interaction and variation of cross-sectional geometry of the wind turbine tower. The pile-water interaction is equivalent to additional mass, the pile-soil interaction is equivalent to linear spring and the cylinder with variable section is equivalent to a multi-section uniform beam in this model. And then the equation is solved by 'fsolve' function in MATLAB. The accuracy and validity of the proposed method are verified against the finite element results. Finally, the influence of foundation depth, upper mass, rotational inertia and pile-water interaction on natural frequency of monopile offshore wind turbine is discussed for practical engineering.
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Key words:
- Offshore wind turbine /
- Monopile /
- Natural frequency /
- Pile-soil interaction /
- Analytical solution
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图 3 桩基础埋深对结构一阶自振频率的影响
Figure 3. Influence of pile length on natural vibration frequency
图 5 上部结构转动惯量对结构一阶自振频率的影响
Figure 5. Influence of rotary inertia on natural vibration frequency
图 6 截面转动惯量对结构一阶自振频率的影响
Figure 6. Influence of section inertia on natural vibration frequency
图 7 桩-水相互作用对结构一阶自振频率的影响
Figure 7. Influence of hydraulic added on natural vibration frequency
表 1 NREL-5MW基准风机刚性地基模型验证
Table 1. Verification of NREL-5MW rigid foundation model
频率验证 频率/rad·s-1 一阶 二阶 三阶 解析解 5.09 23.93 59.94 数值解 5.12 24.14 60.25 误差/% 0.54 0.85 0.52 
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表 2 NREL-5MW基准风机桩-土相互作用模型验证
Table 2. Verification of NREL-5MW pile-soil interaction model
频率验证 频率/rad·s-1 一阶 二阶 三阶 解析解 1.456 10.963 29.210 数值解 1.443 10.725 28.493 误差/% 0.902 2.213 2.515
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表 3 Welney 1S 3.6MW风机桩-土相互作用模型一阶自振频率对比
Table 3. Verification of Welney 1S 3.6MW pile-soil interaction model
频率验证 实测值 Arany等（2015） 解析解 频率/rad·s-1 0.350 0.331 0.3484 误差/% — 5.429 0.457
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