超声速气流中受热壁板的二次失稳型颤振

 研究了超声速气流中受热壁板的非线性气动弹性响应，发现了一种新的动态失稳现象——二次失稳型颤振。基于von Karman非线性应变-位移关系、Reissner-Mindlin板理论和一阶活塞理论建立超声速气流中三维壁板的有限元模型。通过数值算例，研究了超声速气流中受热壁板发生二次失稳型颤振的条件，并运用非线性振动理论分析了二次失稳型颤振的机理。研究表明，超声速气流中受热壁板在平衡态的稳定性未发生变化时，也会因系统参数的变化引起气动弹性响应性质的突变，导致壁板的二次失稳型颤振。二次失稳型颤振能否发生不仅受到气流速压和壁板温升的影响，而且还与初始扰动有关。当扰动引起壁板的初始变形较小时，不能激发出二次失稳型颤振，壁板的气动弹性响应最终收敛到屈曲平衡态。应用二次失稳型颤振理论和分析方法，确定了前人给出的一个金属壁板模型的热颤振边界的风洞试验结果，而且计算结果与试验结果符合良好，从而对这一壁板热颤振现象的风洞试验结果作出了较合理的理论解释。

Secondary Instability Flutter of Heated Panels in Supersonic Airflow

A new dynamic instability phenomenon—secondary instability flutter—is found in the study of nonlinear aeroelastic response of heated panels in supersonic flow. According to the von Karman nonlinear strain-deflection relationship, the Reissner-Mindlin plate theory, and the first order piston theory, a finite element model for the aeroelastic analysis of a heated panel in supersonic airflow is established. The nonlinear aeroelastic response of the panel is calculated numerically. The mechanism of the secondary instability flutter is not due to Hopf bifurcation, but should be interpreted by the catastrophe theory. It is also found that secondary instability flutter will not occur when the perturbed initial deflection of the panel is not large enough, and that it is affected by the initial deflection as well as the aerodynamic pressure and the temperature elevation of the panel. By applying the secondary instability flutter theory and analytical method, the flutter boundary for an aluminum panel which has been tested in a wind tunnel by other researchers is determined. The results agree well with those obtained in the wind tunnel tests. It can be concluded that the proposed secondary instability flutter theory can provide good explanation to the post-buckling thermal flutter of heated panel.