The paper presents a mathematical Single-Degree-of-Freedom model of a cable with ice accretion vibrating in an air flow. It follows an experimental investigation of several aeroelastic models in a wind tunnel. The analysis of the experimental data is very complicated because a number of structural and stream characteristics mutually interact. Distinction between deterministic and random response components is only possible using a theoretical solution. The vibrational movement of the models used can be expressed by van der Pol-Duffing type equations. The aeroelastic excitation that is due to the air flow is modeled as an additive process consisting of a deterministic periodic part and random components. The paper investigates several particular configuration parameter settings for a non-white Gaussian random part of an excitation process and characterizes corresponding response properties. The Fokker-Planck equation is constructed for the random part of the response, and its semi-analytical solution in exponential form is expressed using a probability potential. Partial amplitudes of a harmonic approximation of the response are determined using the stochastic averaging strategy. The existence of a stationary probability distribution of the response is investigated, and its stochastic stability is assessed. Open problems and further research steps are outlined.

本文提出了一种数学模型，该模型具有在空气流中振动的积冰现象的电缆的单自由度模型。它是对风洞中几种空气弹性模型进行的实验研究。实验数据的分析非常复杂，因为许多结构和流特征相互影响。确定性响应组件和随机响应组件之间的区别只有通过理论解决方案才能实现。所用模型的振动运动可以通过范德波尔-达芬类型方程表示。由气流引起的气动弹性激励被建模为一个加性过程，该过程由确定性周期性部分和随机分量组成。本文研究了激励过程中非白色高斯随机部分的几种特殊配置参数设置，并描述了相应的响应特性。针对响应的随机部分构造了Fokker-Planck方程，并使用概率势表示了指数形式的半解析解。使用随机平均策略确定响应的谐波近似值的部分幅度。研究了响应的平稳概率分布的存在，并评估了其随机稳定性。概述了未解决的问题和进一步的研究步骤。并使用概率势表示其半解析解。使用随机平均策略确定响应的谐波近似值的部分幅度。研究了响应的平稳概率分布的存在，并评估了其随机稳定性。概述了未解决的问题和进一步的研究步骤。并使用概率势表示其半解析解。使用随机平均策略确定响应的谐波近似值的部分幅度。研究了响应的平稳概率分布的存在，并评估了其随机稳定性。概述了未解决的问题和进一步的研究步骤。