含间隙舵面非线性动力学分析

为了建立含间隙舵面动力学模型,研究系统的非线性动力学行为,分析系统稳定性及参数对其特性的影响,针对含间隙舵二维动力学模型,采用三阶活塞理论建立了含间隙舵非线性气动弹性动力学方程,应用稳定性分析、Hopf分岔理论和数值方法分析系统的非线性颤振特性,根据求解的复特征根研究系统稳定性,根据特征根曲线分析马赫数和间隙对系统稳定性的影响,并通过Runge–Kutta法求解得到的舵面二维颤振常微分方程组,研究不同来流速度条件下的系统动力学响应。结果表明:间隙舵系统存在临界颤振速度,当来流速度达到临界颤振速度时,系统平衡点失稳,变成具有较大幅值的颤振极限环;此外,临界颤振来流速度随马赫数的增加,先增大后减小,随沉浮间隙量的增大而增大,随俯仰间隙量的增大而减小。

Nonlinear Dynamical Analysis of the Rudder with Gaps

A model of the rudder with gaps is established,and the nonlinear dynamical action influenced by parameters is analyzed.Considered with the two-dimensional dynamical model of the rudder with gaps,the third-order piston theory is used to establish a nonlinear aeroelastic dynamical equation.The stability of the system,Hopf bifurcation theory and numerical methods are used to analyze the nonlinear flutter characteristics of the system.Eigenvalues are solved to study the system stability to analyze the effect of the Mach number and the gap value on the system stability according to the eigenvalue curve.Then the two-dimensional flutter ordinary differential equations of the rudder are obtained by the Runge-Kutta method.Results show that there is a critical flutter velocity in the gap-rudder system.When the increasing velocity reaches the critical one,the system's equilibrium point becomes unstable with a flutter limit cycle with larger amplitude occurred.In addition,the critical velocity of flutter is affected by the Mach number and gap values.The critical flutter velocity exists in the system affected by the Mach number and gap values.