随机扰动下气动弹性系统失稳机理的研究

项目名称： 随机扰动下气动弹性系统失稳机理的研究

项目编号： No.11502067

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 胡栋梁

作者单位： 河海大学

项目金额： 20万元

中文摘要： 气动弹性系统的随机失稳（颤振现象）在航空航天、土木和机械工程领域中是普遍存在的；而且随机颤振的发生通常会位于确定性的颤振点之前，目前对于这种现象的认识还很匮乏。因此气动弹性系统随机稳定性问题的研究具有重要的应用前景和理论意义。基于随机动力学理论以及申请者近6年来在该领域已取得的成果（6篇SCI学术论文），本项目拟研究随机扰动下气动弹性系统的稳定性和分岔行为。利用Khasminskii变换、球坐标变换、FPK算子的特征谱展式、L. Arnold摄动法以及随机平均法等对随机颤振系统的矩Lyapunov指数和最大Lyapunov指数进行求解，定性分析颤振系统的随机稳定性（矩稳定性和样本稳定性），全面刻画颤振系统的随机分岔（D-分岔和P-分岔）行为。此外，通过建立气动弹性系统的随机动力学模型以及分析各类随机因素对颤振系统随机稳定性和分岔行为的影响，从随机动力学角度揭示气动弹性系统的失稳机理。

中文关键词： 随机稳定性；Lyapunov指数；随机分岔；FPK方程；随机颤振

英文摘要： The stochastic instability, i.e., flutter phenomenon, of aeroelastic system is widely observed in a variety of engineering fields such as aerospace, civil and mechanical engineering, just to mention a few. And stochastic flutter always occur before the deterministic flutter point, and so far, there is a deficient knowledge about this phenomenon. Therefore, the investigation of aeroelastic stochastic stability is of great significance in both industrial applications and theoretical research. Based on the stochastic dynamics theory and the achievements of applicant in this field during the past six years as evidenced in my six SCI-indexed papers, the proposal will investigate the stochastic stability and bifurcation behaviors of aeroelastic systems under random perturbations. We will use the Khasminskii transformation, sphere coordinate transformation, the spectrum representation of FPK operator, the perturbation method and the stochastic averaging method to acquire the moment Lyapunov exponent and the maximum Lyapunov exponent of random flutter systems. Then we make qualitative analysis of the stochastic stability (the moment stability and the sample stability) of the system, and describe the stochastic bifurcation behaviors (D-bifurcation behavior and P-bifurcation behavior) of flutter systems in a systematical way. This will also further establish the random dynamic models of aeroelastic systems, and analyze the effect of varied random factors on the stochastic stability and stochastic bifurcation behaviors of flutter systems. The purpose is to reveal the instability mechanism of aeroelastic systems from the perspective of stochastic dynamics.

英文关键词： Stochastic stability;Lyapunov exponent ;Stochastic bifurcation;FPK equation;Stochastic flutter