摘要
采用Galerkin方法建立了超音速气流中二维曲壁板的非线性热气动弹性运动方程.用von Karman大变形理论建立曲壁板的变形与应变的关系.用一阶活塞理论模拟曲壁板上表面受到的气动力.在不同来流速压和温升条件下,用分岔理论研究了具有不同初始几何曲率的曲壁板系统对应的定常状态方程(组)解的个数、性态和动态稳定性,并对方程(组)进行了解曲线的跟踪分析.研究表明,不同条件下方程组的解特性不同,并且随着初始几何曲率和温升条件的变化,二维曲壁板气动弹性系统的失稳机理发生变化.超音速气流中的二维曲壁板系统存在动态Hopf分岔和静态鞍-结点分岔两种失稳现象,但不会发生热屈曲失稳.
An investigation on bifurcation of the curved panel in supersonic air flow is performed in this paper.The nonlinear aeroelastic model for a two-dimensional cylindrically curved panel with constant streamwise curvature is built in supersonic air flow and elevated temperature environment.The vonKarman＇s large deflection plate theory,the quasi-steady first-order piston theory and the quasi-steady temperature distribution are used in the formulation.The Galerkin＇s method has been used to discrete the mathematical model into a set of coupled nonlinear ordinary differential equations.Then these equations are studied by using theories of static bifurcation and Hopf bifurcation.The results show that at different combinations of control parameters such as dynamic pressure,temperature elevation and height-rise of cylindrically curved panel,different static equilibrium positions may exist.And there are two different mechanisms for the instability onset of the curved panel.
出处
《力学学报》
EI
CSCD
北大核心
2010年第5期863-869,共7页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(11072198
10672135)
高等学校学科创新引智计划(B07050)
教育部新世纪优秀人才支持计划(NCET-04-0965)资助项目~~
关键词
曲壁板
分岔
气动弹性
超音速气流
温升
curved panel
bifurcation
inherent geometrical curvature
supersonic air flow
temperature
