Fluttering Behavior of a Flexible Thin Sheet in High Speed Air Flow

在空气中高速移动和/或处理诸如纸、塑料膜、布、薄金属板等的非常薄且柔性的片材的过程被用于许多工业领域。加速这样的过程往往会引起板的颤动，从而对产品质量和生产效率产生不利影响。这种现象被认为是由板弹性行为和气动激励的干扰引起的气动弹性不稳定性（颤振）。为了从理论和实验两方面建立预测和解释这种现象的方法，在小型风洞中进行了前缘固定、后缘自由吹气的纸张试验，收集了各种纸张条件下的颤振速度、频率和模态等实验数据。实验颤振极限被发现形成了一个明确的边界，相对刚度（刚度/动压）与质量比，和振动特性总结的约化频率与质量比。同时，在小扰动假设下，利用流体动力学的分布涡方法和薄板动力学的弹性梁理论，建立了颤振条件的预测方法。用该方法预测的结果与上述实验数据符合得很好，并很好地解释了所观察到的现象的特征。这项研究包括了有关这些问题的实验获得的信息。因此，这项研究，无论是实验的还是理论的，都成功地形成了一个基础，并为评估和解决实际情况提供了一种有用的手段。

Process of moving and/or handling in air at high speed a very thin and flexible sheet of such as paper, plastic film, cloth, thin metal plate, etc. are utilized in many fields of industry. Accelerating such processes tends to cause fluttering of the sheet, thus having adverse effects on the product quality and the production efficiency. The phenomena are considered to be of aeroelastic instability (flutter) induced by the interference of the sheet elastic behavior and the aerodynamic excitation. This investigation aimed to establish a method for prediction and elucidation of the phenomena on both theoretical and experimental bases.Tests were conducted on sheets of papers with the leading edge fixed and the trailing edge freely blown in a small wind tunnel ; experimental data on flutter speeds, frequencies, and modes, etc. were collected for a wide variety of the sheet conditions. The experimental flutter limits were found to form a clear boundary in terms of relative stiffness (stiffness/dynamic pressure) vs.mass ratio, and the vibrational characteristics were summarized in terms of reduced frequency vs.mass ratio..At the same time, a prediction method of the flutter condition was developed utilizing a distributed vortex method for the fluid dynamics and an elastic beam theory for the sheet dynamics on the assumption of small perturbation. Results predicted by the method gave good agreement with the above experimental data and explained well the characteristics of the phenomena observed.It is also necessary to know about the effects of external disturbances tending easily to affect very thin sheets. This investigation includes experimentally obtained informations on such concerns.Thus the investigation, both experimental and theoretical, succeeded in forming a basis and providing a useful means for evaluating and tackling the practical situations.