激波主导流动下壁板的热气动弹性稳定性理论分析

针对激波主导流动下弹性壁板的热气动弹性稳定性分析问题,建立了基于当地活塞流理论的分析模型,并用数值仿真方法来验证其正确性. 首先基于Hamilton原理和Von-Karman大变形理论,建立壁板的热气动弹性运动方程,其中假设壁板受热后温度均匀分布,激波前后区域的气动力模型采用当地一阶活塞流理论;利用Galerkin方法将具有连续参数系统的偏微分颤振方程离散为有限个自由度的常微分方程;基于李雅普诺夫间接法将非线性颤振方程组在平衡位置处进行线化,再用Routh-Hurwits判据来判断线性系统的稳定性,从而来推论出非线性颤振系统的气动弹性稳定性. 在时域中采用龙格--库塔法对非线性颤振方程进行数值积分,得到壁板非线性颤振响应的时间历程,与理论分析结果进行对比. 研究结果表明,壁板受到斜激波冲击时,更容易发生颤振失稳,并且激波强度越大,极限环幅值和频率越大;激波主导流场中的壁板失稳边界不同于传统单纯超声速气流中壁板颤振的失稳边界;只有在斜激波前后不同的动压值都满足颤振稳定性边界的条件下,壁板才可能保持其气动弹性稳定性. 

AEROELASTIC STABILITY ANALYSIS OF HEATED FLEXIBLE PANEL IN SHOCK-DOMINATED FLOWS

In order to analyze the aeroelastic stability of heated flexible panel in shock-dominated flows, a systematic theoretical analysis model is established, and then test its correctness by the numerical simulation method. First of all, based on Hamilton principle and Von-Karman large deflection plate theory, the coupled partial differential governing equations are established with thermal effect based on quasi-steady thermal stress theory. Local first-order piston theory is employed in the region before and after shock waves. The Galerkin discrete method is employed to truncate the partial differential equations into a set of ordinary differential equations. The nonlinear flutter equation is linearized in the equilibrium position based on Lyapunov indirect method,and then Routh-Hurwits criterion is employed to analyze stability of the linear system. Finally, aeroelastic stability of the nonlinear flutter system is obtained. In order to verify the correctness of theoretical results, the nonlinear flutter equations are solved by the fourth-order Runge-Kutta numerical integration method to obtain time history of panel response. The results show that stability of the panel is reduced in the presence of the oblique shock. In other words, the heated panel becomes aeroelastically unstable at relatively small flight aerodynamic pressure. And the LCO amplitude and frequency are observed to increase with shock strength; the stability boundaries of heated flexible panel in shock-dominated flows are distinct from that in regular supersonic flows; only if the non-dimensional dynamic pressure upstream of the shock impingement location and the non-dimensional dynamic pressure downstream of the shock impingement location of the panel satisfy critical condition of flutter stability, will the heated panel be aeroelastically stable.