中文摘要：

研究了具有初始曲率的二维曲壁板在亚音速气流中的分岔问题。考虑大变形和粘弹性的影响,通过模态展开法获得了曲壁板上的静、动态气动压力;采用Galerkin方法将振动控制方程离散为常微分方程组;采用牛顿迭代法求解方程组得到了静变形位置;在参数空间内分析了曲壁板的分岔特性;采用Runge-Kutta方法进行数值计算得到了曲壁板的时程响应相图。结果表明：曲壁板的初始变形会产生静态气动力,并会使得曲壁板产生新的静平衡点位置;当气流动压超过临界动压后,系统将会产生尖点分岔现象,使其平衡点的数目和稳定性发生变化;系统的稳定响应与气流动压及初值有关。

英文摘要：

The bifurcations of two-dimensional curved plate with initial curvature in subsonic flow is studied. Consider- ing the influence of large deflection equation and viscoelasticity. The static and dynamic aerodynamic pressure of curved plate is derived on modal superposition method. The governing partial differential equation is transformed to a series of ordinary dif- ferential equations by using Galerkin method. Solving the equations by Newton iteration method, the position of static deformation is obtained. Bifurcation of the curved plate is studied in a parameter-space, and the Runge-Kutta method is used to calculate the time history response of curved plate phase diagram. The results show that： the initial deformation of the curved plate lead to static aerodynamic force and a new static position, the system will undergoes an imperfect-like bifurcation resulting in the change of the number and the stability of equilibrium points and the steady response to the system is closely related to the dynamic pressure and initial value.