超音速流-热载作用下梯度多孔壁板的非线性振动特性分析

Nonlinear vibration characteristics of a gradient porous wall plate under supersonic flow and heat load

基于Von Kármán薄板大挠度理论和Kirchhoff假设研究梯度多孔薄壁板的非线性振动特性分析。考虑孔隙沿壁板厚度方向呈三种不同分布,采用Galerkin法对梯度多孔壁板进行变换并对气动弦长进行积分得到非线性方程,再利用Hurwitz行列式将Hopf分岔的判定转化为非线性方程的求根,求解出无量纲临界频率和无量纲临界流速。最后通过算例计算,与已有文献得出的结果进行退化和对比,并分析了温度应力、孔隙率、气动刚度系数对梯度多孔薄壁板气动弹性的稳定性影响。

Based on the Von Kármán thin plate large deflection theory and Kirchhoff assumption, the nonlinear vibration characteristics of a gradient porous thin-walled plate were studied. Considering the three different distributions of pores along the thickness direction of the wall plate, the Galerkin method was used to transform the dynamic equation of the gradient porous wall plate and the nonlinear equation was obtained by integrating over the aerodynamic chord length. Then the determination of Hopf bifurcation was transformed into solving the root of the nonlinear equation by using the Hurwitz determinant, and the dimensionless critical frequency and dimensionless critical velocity were thus solved. Finally, a numerical example was calculated and the results were compared with those obtained in the existing literature. The effects of the temperature, stress, porosity and aerodynamic stiffness coefficient on the aeroelastic stability of gradient porous thin-walled plates were analyzed.