初应力截锥壳的气动弹性非线性系统分岔研究

Supersonic Aeroelastic Bifurcation of Nonlinear Truncated Conical Shells with Initial Stress

摘要: 为研究超声速轴向流中具有初应力的完全截锥壳非线性响应问题，采用活塞理论计算气动力，建立了含有初应力的截锥壳非线性气动弹性运动方程。采用一维微分求积法离散，求解了不同初应力状态下，完全截锥壳的气动弹性非线性响应，并考虑了旋转角速度的影响。结果表明，不同初应力对应的Hopf分岔点不同，随着气动压力的增大，初应力对极限环颤振幅值的影响逐渐减弱。在以压应力为参数的响应研究中，没有发现明显的多周期现象，系统在临界压应力之后出现Hopf分岔，极限环幅值随压应力的增大而增大。

Abstract: The influence of initial stress on the nonlinear flutter of circular truncated conical shells in axial supersonic airflow was investigated. The piston theory was used to calculate aerodynamic force. Nonlinear aeroelastic equations of circular truncated conical shells with initial stress terms were established. The nonlinear responses of circular conical shells under different initial stress levels were studied by one dimensional differential quadrature method (DQM), considering the influence of rotating angular speed. The results show that, the influence of initial stress can change the critical aerodynamic pressure of Hopf bifurcation. As the aerodynamic pressure increases, the influence of initial stress on the amplitude of the limited cycle oscillation decreases. No obviously multi-periodic phenomenon was found in the response research with the compressed stress as parameter. The bifurcation is a Hopf type upon the critical compressed pressure. As the compressed stress increases, the amplitude of limited cycle oscillation increases.