Abstract In this paper, the aeroelastic problems of slender vehicles under the influence of random factors and thrust are studied. An aeroelastic dynamic model of a free-free Euler–Bernoulli beam considering thrust and aerodynamic forces is established based on Hamilton’s principle of nonconservative systems. On this basis, considering the influence of random factors, the elastic modulus and viscous drag are regarded as one-dimensional continuous stationary random fields and discretized. The stochastic finite element method is used to solve the dynamic model, and the results are compared with the Monte Carlo simulation results. Then, the influence of the correlation of the random field on the elastic displacement is further analyzed. The following simulation results are obtained: (1) the stochastic factor analysis model established in this paper can reflect the statistical characteristics of aeroelastic response well; (2) the stronger the correlation of the random field is, the greater the expectation of elastic displacement, but as the correlation increases, the expectation tends to be constant; and (3) it is necessary to choose the discrete length of the random field reasonably, and the discrete length depends on the correlation characteristics of the random field studied.

中文翻译：

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受随机因素影响的细长车辆动力学分析

摘要 本文研究了随机因素和推力影响下细长飞行器的气动弹性问题。基于Hamilton非保守系统原理，建立了考虑推力和气动力的自由自由欧拉-伯努利梁的气动弹性动力学模型。在此基础上，考虑随机因素的影响，将弹性模量和粘滞阻力视为一维连续平稳随机场并离散化。采用随机有限元法求解动力学模型，并与蒙特卡罗模拟结果进行比较。然后，进一步分析随机场的相关性对弹性位移的影响。得到如下仿真结果：(1)本文建立的随机因子分析模型能够较好地反映气动弹性响应的统计特征；(2) 随机场的相关性越强，弹性位移的期望越大，但随着相关性的增加，期望趋于恒定；(3)需要合理选择随机场的离散长度，离散长度取决于所研究的随机场的相关特性。