航空学报 > 1988, Vol. 9 Issue (11): 554-577

飞行器壁板颤振的无限维非线性分析

郭乾荣   

  1. 上海交通大学
  • 收稿日期:1987-06-27 修回日期:1900-01-01 出版日期:1988-11-25 发布日期:1988-11-25

AN INFINITE DIMENSIONAL NONLINEAR ANALYSIS OF PANEL FLUTTER

Guo Qianrong   

  1. Shanghai Jiaotong University
  • Received:1987-06-27 Revised:1900-01-01 Online:1988-11-25 Published:1988-11-25

摘要: 一、无限维Hopf分叉定理和中心不变流形定理 由于偏微分方程的矢量场(在任一适当的Banach空间中)常常不是光滑函数,Marsden-McCracken利用(相)流的光滑性提出了流的Hopf分叉定理和中心流形定理。这里的流都是半(相)流,也就是半群。

Abstract: The equation of motion of panel flutter is a nonlinear partial differential equation. It is usually treated approximately by a system of ordinary differential equations. In this paper the author makes an infinite dimensional nonlinear analysis for panel flutter; ( 1 ) using the infinite dimensional Hopf bifurcation theory to find the bifurcation values, and ( 2 ) using center manifold theory to determine the stability of the bifurcating periodic motions.