Raaj Ashwad, Venkatramani J, Mondal Sirshendu
Department of Mechanical Engineering, Shiv Nadar University, Greater Noida 201314, India.
Department of Mechanical Engineering, National Institute of Technology, Durgapur 713209, India.
Chaos. 2019 Apr;29(4):043129. doi: 10.1063/1.5084719.
Interaction of fluid forces with flexible structures is often prone to dynamical instabilities, such as aeroelastic flutter. The onset of this instability is marked by sustained large amplitude oscillations and is detrimental to the structure's integrity. Therefore, investigating the possible physical mechanisms behind the onset of flutter instability has attracted considerable attention within the aeroelastic community. Recent studies have shown that in the presence of oncoming fluctuating flows, the onset of flutter instability is presaged by an intermediate regime of oscillations called intermittency. Further, based on the intensity of flow fluctuations and the relative time scales present in the flow, qualitatively different types of intermittency at different flow regimes have been reported hitherto. However, the coupled interaction between the pitch (torsion) and plunge (bending) modes during the transition to aeroelastic flutter has not been explored. With this, we demonstrate with a mathematical model that the onset of flutter instability under randomly fluctuating flows occurs via a mutual phase synchronization between the pitch and the plunge modes. We show that at very low values of mean flow speeds, the response is by and large noisy and, consequently, a phase asynchrony between the modes is present. Interestingly, during the regime of intermittency, we observe the coexistence of patches of synchronized periodic bursts interspersed amidst a state of desynchrony between the pitch and the plunge modes. On the other hand, at the onset of flutter, we observe a complete phase synchronization between the pitch and plunge modes. This study concludes by utilizing phase locking value as a quantitative measure to demarcate different states of synchronization in the aeroelastic response.
流体力与柔性结构的相互作用往往容易引发动态不稳定性，比如气动弹性颤振。这种不稳定性的起始表现为持续的大幅振荡，对结构完整性有害。因此，研究颤振不稳定性起始背后可能的物理机制在气动弹性学界引起了相当大的关注。近期研究表明，在有迎面波动流存在的情况下，颤振不稳定性的起始由一种称为间歇性的振荡中间状态预示。此外，基于流波动的强度以及流中存在的相对时间尺度，迄今已报道了不同流态下性质不同的间歇性类型。然而，向气动弹性颤振转变过程中俯仰（扭转）和沉浮（弯曲）模态之间的耦合相互作用尚未得到探索。在此，我们用一个数学模型证明，在随机波动流下颤振不稳定性的起始是通过俯仰和沉浮模态之间的相互相位同步发生的。我们表明，在平均流速非常低的值时，响应大体上是有噪声的，因此，模态之间存在相位异步。有趣的是，在间歇性状态期间，我们观察到在俯仰和沉浮模态之间的失同步状态中穿插着同步周期性突发斑块的共存。另一方面，在颤振起始时，我们观察到俯仰和沉浮模态之间完全的相位同步。本研究通过利用锁相值作为一种定量度量来划分气动弹性响应中不同的同步状态而得出结论。
