微型飞行器的仿生力学——蜜蜂悬停飞行的动稳定性研究

研究蜜蜂悬停飞行的纵向动稳定性问题。用数值求解N-S方程的方法计算拍动翅及身体的气动导数;用特征模态分析方法求解运动方程。蜜蜂悬停飞行的纵向扰动运动由3个特征模态构成:不稳定振荡模态、快衰减模态、慢衰减模态。不稳定振荡模态主要为俯仰与水平方向的振荡运动;向前运动伴随上仰运动,向后运动伴随下俯运动,这种水平运动与俯仰运动的耦合产生的与转动方向同向的力矩,是不稳定的原因。快衰减模态主要为单调下俯和向前(或上仰和向后)运动。慢衰减运动主要为下沉(或上升)运动。由于不稳定振荡模态的存在,蜜蜂的悬停飞行是动不稳定的,扰动增长的倍幅时间(0.11s)是拍动周期(5.1ms)的22倍,这对蜜蜂来说是较慢的。这里的结果也许可解释蜜蜂为何悬停得很平稳,同时机动性也很好:扰动增长慢,易于调整翅的运动以抑制之(昆虫可在远小于拍动周期的时间内调整其翅膀的运动);而稳定性弱或不稳定为高机动性提供了基础。

Biomimetic Mechanics of Micro-air Vehicles-Dynamic Flight Stability of a Hovering Honeybee

The longitudinal dynamic flight stability of a hovering honeybee is studied by using the method of computational fluid dynamics to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are employed for solving the equations of motion. The disturbed motion has three natural modes: an unstable oscillatory mode, a stable fast subsidence mode and a stable slow subsidence mode. The unstable oscillatory mode consists of pitching and horizontal moving oscillations with negligible vertical motion; and the coupling of nose-up pitching with forward horizontal motion (and nose-down pitching with backward horizontal motion) in this mode causes the instability. The stable fast subsidence mode consists of monotonic pitching and horizontal motions. The stable slow subsidence mode is mainly a monotonic descending (or ascending) motion. As a result of the unstable oscillatory mode, the hovering flight of the honeybee is dynamically unstable. However, the instability is 'slow' to the honeybee: the time for the initial disturbances to double (0.11 s) is more than 22 times the wingbeat period (5.1 ms). These results may explain why a honeybee can perform steady hovering and at the same time has good maneuverability: slowly growing disturbance can be easily suppressed by adjusting wing motion; and weak stability or instability is required for good maneuverability.