超音速流中二维板的Hopf分叉  

HOPF BIFURCATION OF A TWO-DIMENSIONAL THIN PLATE IN SUPERSONIC AIRFLOW

作　　者：陈大林[1] 杨翊仁[1] 肖世富[2] 胡绍全[2] 

机构地区：[1]西南交通大学应用力学与工程系,四川成都610031 [2]中国工程物理研究院总体工程研究所,四川绵阳621900

出　　处：《工程力学》2008年第4期214-217,共4页Engineering Mechanics

基　　金：国家自然科学基金委与中国工程物理研究院联合基金项目(10576024)

摘　　要：应用Hamilton变分原理建立了对边简支对边自由薄板在超音速流作用下的非线性动力学方程,其中几何非线性采用Von-Kaman几何非线性关系进行描述,气动力采用了活塞理论。然后用Galerkin方法将偏微分方程化为常微分方程,并利用Hopf分叉的代数判据得到了系统临界流速随初始载荷变化的表达式以及颤振频率随初始载荷与临界流速变化的表达式,最后用数值方法进行了验证。The nonlinear dynamic equations of a simple supported two-dimensional thin plate in the supersonic airflow are established through the Hamiltonian variational principle. In the equation, the geometric nonlinear is expressed by the Von Karman＇s thin plate theory and the aerodynamic pressure is expressed by the piston theory. The partial differential equation is turned into an ordinary differential equation by Galerkin method： A new algebraic criterion of Hopf bifurcation is utilized to achieve the analytic expression of critical flow velocity with the initial in-plane load, the flutter frequency with the initial in-plane load and the critical flow velocity. Finally, the Forth order Runge-Kutta numerical method was applied to certify the theories.

关 键 词：HOPF分叉 临界流速 Hamilton变分原理 活塞理论 GALERKIN方法 

分 类 号：V215.3[航空宇航科学与技术—航空宇航推进理论与工程]