Global dynamics and noise-induced transitions for a two-dimensional panel system in subsonic flow

亚音速流中二维壁板系统的全局动力学和噪声诱导的跃迁

A two-dimensional panel in subsonic flow with stochastic excitation is studied by assuming that the aerodynamic pressure contains random pressure fluctuations.Based on the global properties,the sensitivities of system parameters and noise intensities are presented.Firstly,the parameter region with multiple coexisting attractors under different dynamic pressures is obtained.It is found that the coexistence of multiple attractors extensively appears and the basin structure may be complex.Then the periodic time history diagrams are calculated by simulating the random pressure fluctuation as Poisson white noise.The results show that under typical bistable conditions,the noise sensitivity of the subsonic panel system is related to the basin structures and the disposition of the coexisting attractors to the saddle.The transition between two attractors diffuses along the unstable manifold and tends to the position where the basin boundary curvature is relatively large.The findings underscore the importance of global analysis in assessing the noise load carrying capacity,which provides some valuable insights into the safety design of subsonic panel systems.

本文通过考虑随机气动压力波动,模拟了带随机激励的亚音速流中二维壁板的动态行为.基于全局特性,探究了系统对参数和噪声强度的敏感程度.首先,得到了不同动压下多个吸引子共存的参数区域.研究发现,多吸引子共存现象在亚音速壁板系统中广泛存在且伴随着复杂的吸引域结构.然后,将压力波动模拟为泊松白噪声,刻画系统随机轨迹的周期历程,分析噪声诱导的跃迁.结果表明:在典型双稳态情形下,壁板对噪声的敏感程度与域结构和共存吸引子与鞍的相对位置有关.随着噪声强度的增大,噪声诱导的跃迁频繁发生,系统运动状态在两个吸引子间跃出的位置沿不稳定流形扩散,并趋向于分布在域边界曲率相对较大处.研究结果强调了全局分析在评估系统噪声承载能力方面的重要性,同时为亚音速壁板的安全设计提供了理论依据.