带结构刚度非线性的超音速弹翼颤振分析方法研究

提出了带结构刚度非线性的超音速弹翼的颤振分析方法。以非定常可压三维N-S方程为基础，利用NND-LU混合差分格式，Baldwin-Lomax紊流模型，C-H贴体运动网格计算非定常气动力，并和变系数颤振方程耦合，用时间推进求解的方法计算带非线性结构刚度的翼面颤振特性。通过一个带结构刚度非线性的导弹全动翼面的算例，计算研究了3种常见的结构刚度非线性(间隙型，转折型，三次型)对颤振特性的影响。计算结果表明，间隙型的刚度非线性使颤振速度下降。转折型和三次型刚度非线性能提高额振速度。在一定的速度范围内带结构刚度非线性的颤振系统可能出现极限环振荡。

An Investigation of Flutter Characteristics of Wing with Nonlinear Stiffness in Supersonic Flow

We present a method of analyzing flutter characteristics of wing with nonlinear stiffness in supersonic flow. We calculate the unsteady aerodynamics by 3D N S (Navier Stokes) equations, with NND (non oscillatory, non free parameter, dissipative) difference scheme, LU (lower upper) implicat time advancing scheme, B L (Baldwin Lomax) turbulence model, and C H moving grid. Fig.1 shows the computation flowchart. Section 3 takes as numerical example a missile wing surface that can be used to control. We solve for the structure responses of wing by coupling the N S equations and flutter equations with variable stiffness coefficients. We investigate the influence of three types of nonlinear stiffness on flutter characteristics. Figs.3(a) and 3(b) show the time histories of structure responses of wing for free play type of nonlinear stiffness; Figs.4(a) through 4(d) show those for turn type of nonlinear stiffness. Figs.5(a) through 5(f) show the phase plane figures for cubic type of nonlinear stiffness. The calculated results show that: (1) flutter speed decreases for system with free play type of nonlinear stiffness; (2) flutter speed increases for system with turn type and cubic type of nonlinear stiffness; (3) in genearal, there is the limit cycle oscillation in certain speed range, when the flutter system is influenced by nonlinear stiffness; meanwhile, the shapes of the limit cycles are much different.