柔性对柔性翼弹性支撑于前缘处的pitch-heave颤振不稳定性的影响
Effect of flexibility on the pitch-heave flutter instability of a flexible foil elastically supported on its leading edge
AI总结：
本文研究了柔性翼弹性支撑于前缘处的pitch-heave颤振不稳定性，通过分析工具确定了参数区域，揭示了刚度和重力对稳定性的影响，以及柔性翼与弹簧不稳定性模式的耦合效应。
摘要：
本文提出了一种分析工具，用于计算二维柔性翼弹性支撑的颤振不稳定性参数区域。该工具基于一种新的分析公式，适用于翼浸入无粘性流体中的小振幅振荡和变形。该公式扩展了之前的分析，通过包含重力和第二个弯曲模式的影响，将有效性范围扩展到更小的刚度。分析结果通过现有数值结果验证，捕捉到第一个两个自然弯曲模式，直到刚度参数S的值约为10^-1。当只允许被动垂荡或只允许被动摆动时，刚性翼是稳定的，存在一个上刚度界限，对于弯曲不稳定性，当弹簧刚度增加时，这些不稳定性与弹簧不稳定性模式耦合，增加增长速率。耦合的弹簧（线性或扭振）和弯曲不稳定性模式在S的阈值值以下和R的阈值值以上发生，两者均取决于相应的弹簧刚度。刚性翼的耦合pitch-heave颤振不稳定性出现在由两个弹簧刚度参数平面的曲线所界定的区域中，该曲线依赖于R，当R减小时，该曲线缩至零。对于柔性翼，当S从无穷大减小时，弯曲不稳定模式与弹簧不稳定模式耦合，扩大了颤振不稳定的质量比范围，并增加其增长速率，特别是当弹簧刚度减小时更明显。颤振不稳定的参数区域可以很容易地用当前分析工具来表征，提供相应的频率和临界颤振速度。本文结果可以作为未来基于柔性振荡翼的涡轮机设计的指导。
英文摘要：
An analytical tool is presented to compute the parametric regions of flutter instabilities of a two-dimensional flexible foil elastically mounted. It is based on a new analytical formulation of the unsteady fluid-estructure interaction valid for small-amplitude oscillations and deformations of the foil immersed in an inviscid fluid. The formulation extends a previous analysis by including the effects of gravity and a second flexural mode, increasing its validity range to much smaller rigidities. The analytical results are validated with available numerical results, capturing the first two natural flexural modes down to values of the stiffness parameter $S$ of order $10^{-1}$. When only passive heave, or only passive pitch, is allowed, the rigid foil is stable, existing an upper stiffness bound for the flexural instabilities, wich become coupled with the spring instability mode for small spring constant increasing the growth rate. These coupled spring (linear or torsional) and flexural instability modes occur below a threshold value of $S$ and above a threshold value of $R$, both depending on the corresponding spring constant. Coupled pitch-heave flutter instabilities of a rigid foil occur in a region below a curve of the parametric plane of the two springs constants that depends on $R$, which shrinks to zero as $R$ decreases. For a flexible foil, the flexural unstable modes become coupled with the springs unstable mode as $S$ decreases from infinity, enlarging the mass ratio range for flutter instability and increasing its growth rate, the more so the smaller the springs constants. The parametric regions for flutter instabilities are easily characterized with the present analytical tool, providing the corresponding frequency and critical flutter velocity. The present results can be useful as a guide in the design of future turbines based on flexible oscillating foils.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
