中文摘要：

采用多项式迟滞非线性模型建立二元机翼气动弹性运动方程，并用数值积分法进行求解。通过系统响应振幅随来流速度变化的分叉图和频谱分析发现，俯仰方向由于含有非线性因素，振动中的高阶分量随速度提高不断增加，并引起高次分叉。重点研究“机翼／空气”质量比以及“沉浮／俯仰”两个自由度的自然振动频率比对非线性颤振速度边界的影响，并提出可以通过提高自然振动频率比来减小迟滞非线性因素的不利影响。

英文摘要：

The dynamical equation of a two-dimensional airfoil with polynomial hysteresis nonlinearity in pitch is solved using Runge-Kutta time marching integration. Firstly, the bifurcation diagrams and power spectral densities of pitch and plunge motion are obtained;and it is found that as the existence of nonlinearity there are a number of frequency peaks in the spectrum, which lead to the bifurcation of the pitch amplitude. Then, the effects of airfoil/air mass ratio and plunge/pitch natural frequency ratio on flutter boundary are studied. The resuits show that in order to increase the nonlinear flutter speed,larger plunge/pitch natural frequency ratio can be used.