The production of wingbeat motion of flapping wing hovering flight are determined by the actuating, aerodynamic and inertia forces/moments, which influence the dynamic unsteadiness and controllability of flapping wing flying. This paper presents the feasible solution for cracking the problem of two degrees of freedom (two DoFs, namely, flapping and pitch motion, respectively) highly coupled nonlinear hovering wingbeat dynamics. Firstly, two DoFs nonlinear hovering wingbeat dynamic ordinary differential equations (ODEs) are derived on basis of the extended quasi-steady aerodynamic and inertial forces/moments model. Then, we perform their numerical solution by using tractable ODEs numerical algorithm, boundary value problem-solving format, and least square method. The numerical results have a good consistency with those measured by Dr. Muijres. Moreover, the adjustable rule of phase offset of wing pitch angle relative to the flapping angle is quantificationally studied by introducing frequency ratio between pitch frequency and flapping frequency. We find that the phase offset can be directly regulated by wing pitch hinge stiffness or indirectly modulated by frequency ratio, and the peak value of wing pitch angle monotonously decreases with the increase of wing pitch hinge stiffness, opposite to the angle of attack (AoA). This adjustable rule paves a useful way for the bio-inspired flapping wing micro aerial vehicle (FWMAV) featuring passive or semi-passive pitch flexible hinge to maintain high variable AoA.

拍打翼盘旋飞行的翼拍运动的产生是由驱动力，空气动力和惯性力/力矩决定的，它们影响拍打翼飞行的动力不稳定和可控性。本文提出了解决两个自由度（两个自由度，分别是拍打和俯仰运动）高度耦合的非线性悬停翼拍动力学问题的可行解决方案。首先，在扩展的拟稳态气动和惯性力/力矩模型的基础上，推导了两个自由度非线性悬停的翼拍动力常微分方程（ODE）。然后，我们使用易处理的ODE数值算法，边值问题求解格式和最小二乘法来执行它们的数值解。数值结果与Muijres博士测量的结果具有很好的一致性。此外，通过引入俯仰频率与拍打频率之间的频率比，定量研究了机翼俯仰角相对于拍打角的相位偏移的可调规律。我们发现相位偏移可以直接由机翼变桨铰链刚度来调节，也可以由频率比间接调节，并且随着俯仰角铰链刚度的增加，机翼俯仰角的峰值单调减小，与迎角（AoA）相反。 。这种可调节的规则为生物启发式拍打翼微型航空飞行器（FWMAV）铺平了一条有用的途径，该飞行器具有被动或半被动俯仰柔性铰链以维持高可变AoA。通过引入俯仰频率与襟翼频率之间的频率比，定量研究了机翼俯仰角相对于襟翼角的相位偏移的可调规律。我们发现相位偏移可以直接由机翼变桨铰链刚度来调节，也可以由频率比间接调节，并且随着俯仰角铰链刚度的增加，机翼俯仰角的峰值单调减小，与迎角（AoA）相反。 。这种可调节的规则为生物启发式拍打翼微型航空飞行器（FWMAV）铺平了一条有用的途径，该飞行器具有被动或半被动俯仰柔性铰链以维持高可变AoA。通过引入俯仰频率与襟翼频率之间的频率比，定量研究了机翼俯仰角相对于襟翼角的相位偏移的可调规律。我们发现相位偏移可以直接由机翼俯仰铰链刚度调节，也可以通过频率比间接调节，并且随着俯仰角铰链刚度的增加，机翼俯仰角的峰值单调减小，与迎角（AoA）相反。这种可调节的规则为生物启发式拍打翼微型航空飞行器（FWMAV）铺平了一条有用的途径，该飞行器具有被动或半被动俯仰柔性铰链以维持高可变AoA。机翼俯仰角的峰值随机翼俯仰铰链刚度的增加而单调降低，与迎角（AoA）相反。这种可调节的规则为具有被动或半被动俯仰柔性铰链以维持高可变AoA的生物启发式襟翼微型飞行器（FWMAV）铺平了一条有用的途径。机翼俯仰角的峰值随机翼俯仰铰链刚度的增加而单调降低，与迎角（AoA）相反。这种可调节的规则为生物启发式拍打翼微型航空飞行器（FWMAV）铺平了一条有用的途径，该飞行器具有被动或半被动俯仰柔性铰链以维持高可变AoA。