论文标题
膜上由表面重力波的辐射引起的膜颤动
Membrane flutter induced by radiation of surface gravity waves on a uniform flow
论文作者
论文摘要
我们认为，弹性膜的稳定性位于有限深度的自由度深度的均匀水平流动的底部。膜仅支撑在铅和后边缘，这些边缘将其连接到水平刚性地板的两个部分。该膜的跨度沿垂直于流动方向的方向和流动方向有限长度。对于无限长度的膜，我们得出了一个完整的分散关系，该关系对于流体层的任意深度有效，并找到由于表面重力波的发射而导致膜颤动的条件。我们通过分散性关系根的扰动理论和负能波的概念来描述这种辐射引起的不稳定性，并讨论了其与异常多普勒效应的关系。
We consider stability of an elastic membrane being on the bottom of a uniform horizontal flow of an inviscid and incompressible fluid of finite depth with free surface. The membrane is simply supported at the leading and the trailing edges which attach it to the two parts of the horizontal rigid floor. The membrane has an infinite span in the direction perpendicular to the direction of the flow and a finite length in the direction of the flow. For the membrane of infinite length we derive a full dispersion relation that is valid for arbitrary depth of the fluid layer and find conditions for the flutter of the membrane due to emission of surface gravity waves. We describe this radiation-induced instability by means of the perturbation theory of the roots of the dispersion relation and the concept of negative energy waves and discuss its relation to the anomalous Doppler effect.
