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气动弹性模型中的参数不确定性一般具有一定的分布规律,为了定量分析随机型参数不确定性对颤振的影响特性,考虑气动弹性系统中广义刚度的随机型不确定性,基于浸入式随机多项式展开(PCE)方法,在传统的颤振求解方法——p-k法的基础上,提出了针对不确定性气动弹性系统稳定性分析的增广p-k法——PCEPK(Polynomial Chaos Expansion with p-k)法,并将该方法应用到某机翼的颤振分析中,研究了均匀分布下的广义刚度不确定性对颤振边界的影响,并同基于结构奇异值μ理论的鲁棒颤振分析的结果和计算效率进行了对比。最后,采用标准的蒙特卡罗模拟(Monte Carlo Simulation,MCS)方法验证了结果的正确性。研究结果表明,PCEPK法计算的颤振边界范围是该分布下的“确定”结果,不因随机样本数而改变,克服了随机方法依赖样本数的缺点。同时,与基于结构奇异值理论的鲁棒颤振分析方法相比,它能够考虑不确定性参数分布对颤振特性的影响,具有更广泛的适用范围。
In order to quantitatively analyze the influence of random parameter uncertainty on chatter vibration, the uncertainty of the parameters in the aeroelastic model generally has a certain distribution. Considering the random type uncertainty of generalized stiffness in aeroelastic systems, Polynomial Chaos Expansion with pk method based on Polynomial Expansion (PCE) method is proposed based on traditional chatter solving method - pk method. The method is applied to the flutter analysis of a wing, and the influence of the generalized stiffness uncertainty under uniform distribution on the flutter boundary is studied. The results of the robust flutter analysis based on the theory of structure singular value μ Comparisons with computational efficiency. Finally, the correctness of the results is verified by a standard Monte Carlo Simulation (MCS) method. The results show that the range of flutter boundary calculated by the PCEPK method is the “definite” result of this distribution, and it does not change due to the number of random samples. This overcomes the shortcomings of random method dependent on the number of samples. At the same time, compared with the robust flutter analysis method based on the theory of structure singularity, it can consider the influence of the uncertainty parameter distribution on flutter characteristics and has a wider application range.