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曲壁板在超音速气流中的分岔特性

Bifurcation of the Curved Panel in Supersonic Air Flow

  • 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大变形理论来考虑曲壁板的大变形。用准定常的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,基于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)的解的个数、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,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。

     

    Abstract: 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 curved panel with constant stream-wise curvature is built in supersonic air flow and elevated temperature environment. The Von-Karman’s large deflection plate theory, the quasi-steady first-order piston theory and the quasi-static temperature distribution are used in the formulation. The Galerkin’s method has been used to reduce the mathematical problem to a set of coupled nonlinear ordinary differential equations. Then the nonlinear ordinary differential equations are studied by using static bifurcation and Hopf bifurcation. The results show that at different combinations of control parameters dynamic pressures, temperature elevation and height-rise of the panel, different static equilibrium positions may coexist. And there are two different mechanisms of the instability onset of curved panel.

     

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