In this study, we numerically examine the effect of wing flexibility on the lift force generated by a modeled flapping wing that simulates an insect flight in hover mode. The flow field around the flapping wing is assumed to be two-dimensional (2D), and the flow equations are formulated with the notion of “immersed boundary” for easy handling of the moving-boundary problem. In the 2D framework, the wing chord is treated as an elastic filament. To account for the large deformation in the wing, the motion of the filament is modeled using a geometrically nonlinear equation for bending beams. Both sets of equations are then solved according to the fluid–structure interaction concept using appropriate numerical schemes. Time variation of lift force on the wing is calculated for different values of wing flexural rigidity. Effects of elastic deformation of the wing and interactions between the bending wing and vortical flow structure are discussed. Flexural rigidity that gives the highest average lift force on the wing is sought. This study affirms that the flexibility of wing and the vortex-pair capture phenomenon are crucial to the lift force generation in the flapping-wing mechanics.

中文翻译：

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机翼柔度对悬停模式下二维模型昆虫翅膀拍动产生的升力的影响

在这项研究中，我们用数值方法研究了机翼灵活性对模拟昆虫在悬停模式下飞行的扑翼产生的升力的影响。假设扑翼周围的流场是二维的（2D），并用“浸没边界”的概念制定流动方程，以便于处理移动边界问题。在二维框架中，翼弦被视为弹性细丝。为了解释机翼的大变形，使用弯曲梁的几何非线性方程对灯丝的运动进行建模。然后使用适当的数值方案根据流固耦合概念求解两组方程。针对不同的机翼抗弯刚度值计算机翼升力的时间变化。讨论了机翼弹性变形的影响以及弯曲机翼与涡流结构之间的相互作用。寻求在机翼上提供最高平均升力的抗弯刚度。这项研究证实了机翼的柔韧性和涡对捕获现象对于扑翼力学中升力的产生至关重要。