一类完全锥壳的超声速气动弹性响应问题

Supersonic Aeroelastic Response of Circular Conical Shells

摘要: 为研究超声速轴向流中完全锥壳的气动弹性非线性响应，本文采用活塞理论计算超声速气动力，利用截锥壳的非线性气动弹性运动方程，在截锥壳顶角不为零，小半径无限趋近于零的特定边界条件下，采用一维微分求积法(DQM)离散，数值逼近求解了完全锥壳的颤振临界动压及气动弹性响应。结果表明，不同边界条件对完全锥壳气动颤振临界动压和极限环幅值的影响不大，最小颤振临界对应周向波数相对较小。当动压参数较大时，数值模拟结果显示，顶端自由，底端固支的锥壳还存在一种半稳定的高阶响应极限环，该极限环对应的振幅最大点更靠近锥壳底端。

Abstract: A study on the nonlinear flutter of circular conical shells in axial supersonic airflow was presented. The piston theory was used to calculate aerodynamic force. Nonlinear aeroelastic equations of circular truncated conical shells were used, when the truncated conical shell angle is not zero and the smaller radius is infinitely close to zero. Under this specific boundary conditions, the flutter critical aerodynamic pressures and nonlinear response of circular conical shells were investigated with one dimensional DQM (differential quadrature method). The results show that, the influence of different boundary conditions on the critical dynamic pressure and the limit cycle amplitude of the circular conical shell is not significant.The wave number corresponding to the minimum critical flutter aerodynamic pressure is relatively small. When the dynamic pressure parameters are large, the numerical simulation results show that there is a semi stable high order limit cycle, which maximum point is closer to the bottom of the cone shell.