含高次结构非线性的气动弹性系统随机P-分岔分析

In aircraft design, the aeroelastic coupling between structure and airflow must be thoroughly analyzed to avoid and suppress the flutter. The study of aeroelastic systems with random disturbances is a hot and difficult topic in academia. Generally, the study of aeroelastic problems is based on simplified models, and turbulence disturbances are neglected in the process of modeling, which leads to a great difference between the research results and engineering. An analytical aeroelastic system dynamics model will be established for high-dimensional stochastic aeroelastic systems, considering the structural nonlinearity of the wing and the randomness of turbulent disturbances.On the basis of dimension reduction, the semi-analytical method of stochastic dynamic system and numerical simulation are used to understand the stochastic and non-linear dynamic behavior of stochastic aeroelastic system.Considering the requirement of large critical flutter velocity prediction in engineering practice, based on the stochastic P-bifurcation analysis method of high-dimensional and multi-dimensional steady-state systems, we will provide a new perspective for predicting the nonlinear critical flutter velocity of stochastic aeroelastic systems.The outcome of this research will make the field of stochastic dynamics of aeroelastic systems more colorful, and will build the theoretical basis for engineering problem.

在飞行器设计中,必须深入分析结构与空气之间的气动弹性耦合,避免和抑制由此产生的颤振。含随机扰动气动弹性系统相关问题的研究是学术界的热点和难点，对气动弹性问题的研究一般都基于简化模型,建模过程中忽略湍流扰动，导致研究结果与工程有较大差异。项目针对高维随机气动弹性系统，结合翼面本身的结构非线性特点，考虑湍流扰动，建立解析形式的气动弹性系统动力学模型。对所建立的含随机扰动3自由度机翼动力学方程，在降维的基础上应用随机动力学系统的半解析方法，结合数值模拟，更加深入认识随机气动弹性系统的随机、非线性动力学行为。考虑到工程实际中对大幅临界颤振速度预测的需求，基于高维多稳态系统随机P-分岔分析方法，项目将提供一种预测随机气动弹性系统非线性临界颤振速度的全新视角。这些研究工作将丰富气动弹性系统随机动力学的研究成果，并能为其在现代航空工程领域的应用提供参考。

含随机扰动气动弹性系统相关问题的研究是学术界的热点和难点。项目针对高维随机气动弹性系统，结合翼面本身结构非线性特点,考虑湍流扰动，对3-Dof机翼颤振系统随机P-分岔及大幅度临界颤振速度预测等问题开展了系列研究，完成了项目全部研究内容和计划任务，取得了项目预期成果。包括：.(1)考虑二维湍流场，Dryden湍流模型，建立了解析形式非定常气动力模型；考虑高次结构非线性、纵向和垂向湍流扰动，建立了3-Dof机翼颤振系统的非线性随机气动弹性动力学模型。.(2)综合应用确定性降维平均、随机平均法、奇异性理论，发展了适用于随机非线性气动弹性问题的降维分析方法。以具有高次结构非线性的3-Dof带操纵面机翼为对象，研究了其二次分岔、随机P-分岔、大幅极限环振荡等随机非线性动力学行为。.(3)应用高维系统随机P-分岔分析方法讨论了3-Dof机翼颤振系统线性、非线性临界颤振速度的变化规律。应用奇异性分析理论推导了随机P-分岔临界参数条件，得到了大幅随机临界颤振速度随主要参数的变化规律。.本项研究成果丰富了气动弹性系统随机动力学的研究内容，并为随机气动弹性系统非线性临界颤振速度预测等工程实际问题的解决提供了理论参考和技术支持。