Dynamic response analysis of wind turbine towers plays a pivotal role in their analysis, design, stability, performance and safety. Despite extensive research, the quantification of general dynamic response remains challenging due to an inherent lack of the ability to model and incorporate damping from a physical standpoint. This paper develops a frequency adaptive framework for the analysis of the dynamic response of wind turbines under general harmonic forcing with a damped and flexible foundation. The proposed method is founded on an augmented dynamic stiffness formulation based on a Euler-Bernoulli beam-column with elastic end supports along with tip mass and rotary inertia arising from the nacelle of the wind turbine. The dynamic stiffness coefficients are derived from the complex-valued transcendental displacement function which is the exact solution of the governing partial differential equation with appropriate boundary conditions. The closed-form analytical expressions of the dynamic response derived in the paper are exact and valid for higher frequency ranges. The proposed approach avoids the classical modal analysis and consequently the ad-hoc use of the modal damping factors are not necessary. It is shown that the damping in the wind turbine dynamic analysis is completely captured by seven different physically-realistic damping factors. Numerical results shown in the paper quantify the distinctive nature of the impact of the different damping factors. The exact closed-form analytical expressions derived in the paper can be used for benchmarking related experimental and finite element studies and at the initial design/analysis stage.

风力涡轮机塔架的动态响应分析在其分析，设计，稳定性，性能和安全性中起着至关重要的作用。尽管进行了广泛的研究，但从物理角度来看，由于固有的建模和合并阻尼能力的固有缺陷，一般动态响应的量化仍然具有挑战性。本文建立了一个频率自适应框架，用于分析具有阻尼和柔性基础的风力发电机在一般谐波强迫下的动态响应。所提出的方法基于基于具有弹性端部支撑的Euler-Bernoulli梁柱的增强动态刚度公式，以及由风力涡轮机机舱产生的尖端质量和旋转惯性。动态刚度系数是从复值先验位移函数得出的，复函数是具有适当边界条件的支配偏微分方程的精确解。本文得出的动态响应的闭式解析表达式对于较高的频率范围是准确且有效的。所提出的方法避免了经典的模态分析，因此不需要模态阻尼因子的临时使用。结果表明，风轮机动态分析中的阻尼被七个不同的实际阻尼因子完全捕获。本文显示的数值结果量化了不同阻尼因子影响的独特性质。