中文摘要：

采用Galerkin方法建立二维壁板的非线性气动弹性运动方程,用一阶活塞理论模拟壁板受到的气动力.基于李雅普诺夫间接法分析了平壁板的稳定性,得到了壁板失稳的边界曲线;采用牛顿迭代法分析了壁板的屈曲变形,进而分析了后屈曲状态下壁板的稳定性;在时域中分析了后屈曲状态下壁板的颤振边界.分析结果表明,为了保证计算精度,在二维壁板的静态失稳及过屈曲变形分析中,至少要取二阶谐波模态;在平壁板的超音速颤振（动态失稳）边界分析中至少应取四阶模态.还对壁板的温升,壁板长厚比、壁板密度和气流马赫数作了无量纲变参分析,研究了这些参数的变化对壁板稳定性的影响规律.研究中发现,当气流速压较低时壁板一般会稳定在低阶谐波模态的屈曲变形位置,但是如果系统出现多个渐近稳定的不动点,即使作用在壁板上的气流速压很低,壁板也有可能在较低速压下发生二次失稳型颤振.

英文摘要：

　An investigation on stability of heated panels in supersonic air flow is carried out in this paper. A nonlinear aeroelastic model for a two-dimensional heated panel is established using Galerkin method.The quasi-steady piston theory is employed to calculate the aerodynamic load on the panel and the even temperature field is considered.At first,the static and dynamic stabilities for flat panels are studied by using Lyapunov＇s indirect method and the stability boundary curve is obtained.Then the static deformation of a post-buckled panel is calculated by Newton iterative approach,and the local stability of the post-buckling equilibrium is analyzed.The results show that a two-mode model is suitable for panel static stability analysis and static deformation calculation;but more than four modes are required for dynamic stability analysis.The effects of temperature elevation and non-dimensional parameters related to panel length/thickness ratio,material density and Mach number on the stability of heated panels are also investigated.It is found that panel flutter（secondary instability）may occur at relatively low aerodynamic pressure when there are several stable equilibrium points for the aeroelastic system of heated panels.