受限亚音速气流中倒置悬臂壁板静气弹稳定性的理论及实验研究

板壳结构在航空航天、高速列车、能量采集等诸多工程领域已经得到了广泛应用. 将悬臂壁板倒置于轴向气流中并在壁板周围流场中设置刚性壁面可有效地调控壁板的失稳速度, 是俘能器优化设计的重要措施之一. 但针对刚性壁面作用下亚音速气流中倒置悬臂壁板的失稳机制仍需要开展深入研究. 本文以受限亚音速气流中倒置的二维悬臂壁板为对象, 以理论分析及风洞实验为手段, 研究了单侧刚性壁面效应对倒置悬臂壁板静态失稳特性的影响规律. 在理论分析中, 首先应用镜像函数法来处理壁面约束条件, 基于算子理论研究获得了以Possio积分方程为表征的壁板气动力, 壁面效应实际表征为一包含移位Tricomi算子的复合算子; 然后将壁板失稳方程的求解问题转化为定区间上的函数逼近问题; 最后, 依据Wererstrass定理并利用最小二乘法求解该最优函数, 以获得系统的失稳临界参数. 在试验研究中依据压杆稳定原理设计了壁板静态失稳的测试方法并完成了风洞实验. 理论分析结果表明, 壁板会发生发散(静气动弹性)失稳, 临界动压随壁板与壁面间距的增加而增大并最终趋于稳定(无壁面情况); 通过理论与风洞实验结果的对比分析, 验证了本文气动力及理论分析的适用性及准确性. 针对倒置悬臂壁板结构的气动弹性失稳问题, 本文提出的方法不涉及系统方程的离散及特征值求解问题, 而是将其转化为了定区间上的函数逼近问题进行求解, 这为弹性结构静气动弹性失稳问题的研究提供了一个可行的新思路. 

A THEORETICAL AND EXPERIMENTAL STUDY ON THE STATIC AERO-ELASTIC INSTABILITY OF AN INVERTED CANTILEVERED PLATE IN A CONFINED SUBSONIC FLOW 1)

The plate and shell structures have been widely used in many engineering areas such as aerospace, high-speed trains and energy harvesting. An inverted cantilever plate in an axial airflow confined by a rigid wall has the adjustable critical airflow velocity and is one of the most important ways for the optimization of energy harvesters. However, the mechanism of instability of inverted cantilever plates in rigid wall effect still needs further studies. This paper aims at the static aero-elastic instability of an inverted cantilevered plate in a confined subsonic flow, and such problem is studied by both the theoretical and the experiment analysis. In theory, first the effect of rigid wall is modelled by using the mirror image function and the fluid force on the plate is presented as a Possio integral equation within the frame work of differential operators, and the wall effect is featured by a composite operator involving the shifted Tricomi operator; then the solution of the instability equation is changed into the problem of approximation of function at a given interval; and finally the optimal solution is obtained by using the least square method with the help of the Wererstrass theorem. In experimental analysis, a test method for the static instability of the plate developed from the theory of column is applied for the wind tunnel test. The theoretical results show that the plate experiences the static aero-elastic instability; the critical dynamic pressure increases with the the increasing spacing between the wall and the plate but finally becomes steady (the case without rigid wall). A comparison of the present theoretical results with other existing theory and the experiment shows that the present theory is reliable and accurate. In this paper, the instability problem, which is not solved with the discretization of partial differential equation and by the eigenvalue analysis, has been transformed into the problem of approximation of function, and this can serve as another new thinking way to the problem of static aero-elastic instability of plates.