初始角度对平板自由下落运动的影响

平板的自由下落是一个经典的流体力学-动力学耦合问题，且具有明显的非线性特性.针对二维平板自由下落的非线性特性，文章通过耦合求解N-S方程和运动方程，以期认识其非线性特征.从不同初始角度对平板自由下落状态和轨迹的影响出发，分析了运动状态的相轨线和频谱特性，以及其中的非线性系统特征.研究发现，在平板自由下落初期，不同初始角度下平板呈现不同的运动状态和轨迹，常为非周期性摆动或小幅翻滚运动.在自由下落后期，平板自由下落最终呈现周期性摆动或翻滚运动，运动模态归为一致，初始角度对该模态没有影响. 

Influence of Initial Angle on the Freely Falling Plates

The free fall of plates is a classic problem of fluid mechanics-dynamics coupling, which has obvious nonlinear characteristics. According to the nonlinear characteristics of 2D freely falling plates, the equations of motion coupled with the Navier-Stokes equations were numerically solved in this paper. The motion states and trajectories of freely falling plates at different initial angles were compared, and characteristics of the nonlinear system were studied with phase trajectories and spectrum analysis method. The research results indicate that there are differences on motion states and trajectories with different initial angles in initial stage of free fall, and these motions are non-regular fluttering and small-amplitude tumbling. However, the motions finally turn into periodic fluttering or tumbling in later stage of free fall. The initial angle has little effect on the motion mode.