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

在空气中高速移动和/或处理非常薄和柔软的薄板的过程，如纸、塑料薄膜、布、薄金属板等，在许多工业领域中都有使用。加速这样的过程往往会导致板材的抖动，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薄板弹性行为和气动激励的干扰引起的气动弹性不稳定(颤振)。本研究旨在建立一种从理论和实验两方面预测和解释这一现象的方法。在小型风洞中，在前缘固定、后缘自由吹动的纸片上进行试验，收集了各种纸片条件下的颤振速度、频率和振型等实验数据。实验结果表明，颤振极限以相对刚度(刚度/动压)与质量比成明显的界限，并用频率与质量比的折减来概括颤振特性，同时，在小扰动假设下，利用流体动力学的分布涡法和薄板动力学的弹性梁理论，建立了颤振状态的预报方法。用该方法预测的结果与上述实验数据吻合较好，很好地解释了观察到的现象的特点。此外，还需要了解外部干扰的影响，这些干扰往往会影响很薄的薄板。这项调查包括通过实验获得的有关这类问题的信息。因此，这项实验和理论调查成功地为评估和解决实际情况奠定了基础和提供了有用的手段。

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.