二元非线性机翼随机动力学行为

 为考查在高斯白噪声作用下二元机翼随机颤振动力学行为，采用数值仿真的方法对其进行了研究。首先把机翼简化成一个具有扭转和上下自由度的平板,其中扭转弹簧具有3次非线性刚度,同时假设空气是线性不可压的而且气动力是定常的,再对任意运动和高斯白噪声作用下的机翼进行建模。其次采用了蒙特卡罗仿真来求解随机微分方程的数值解,根据数值解结果进行统计分析,计算出最大Lyapunov指数。最后得出：在随机激励作用下机翼的动力学行为与确定性颤振相比有很大差异,同时随机颤振点提前于确定性颤振点。

On Stochastic Dynamical Behaviors of Binary Airfoil with Nonlinear Structure

This article examines the dynamical behavior of stochastic flutter of binary airfoil that is excited by a Gauss white noise by means of numerical simulation. Firstly, the airfoil is modeled as a flat plate in a linear constant incompressible flow under a Gauss white noise excitation. The plate is with two degrees of freedom on heave and pitch and with a structural type nonlinearity in the form of a cubic hardening torsional spring. Secondly, a Monte Carlo simulation is performed to solve the system of random differential equations. And then based on the numerical result, a statistic analysis is made and the maximal Lyapunov exponent of the relevant system is obtained. Finally, it is found that the dynamical behavior of a nonlinear structural airfoil excited by a Gauss white noise is dramatically different from that of a deterministic system and its stochastic flutter point is always ahead of the point of the deterministic flutter.