We present a numerical and experimental study on the static-divergence instability of an inverted cantilevered plate in an uniform axial subsonic airflow. The flow is assumed ideal and is confined by a rigid channel wall. The inverted cantilevered plate, unlike a conventional one, is with a clamped trailing edge and a free leading edge. The equation of the plate motion is solved by the finite-difference method, and the linearized boundary element method is applied for the fluid equations. A new trigonometric form vortex panel model is developed for the solution of fluid force. An equivalent test method is developed for the divergence instability and is applied for the experimental study. The effect of the rigid wall is evaluated for various distances between the plate and the rigid channel wall, and the critical airflow velocity increases with the increase in the distance. The numerical calculations and predication show good agreement with the experimental results. When the distance is large enough, the numerical results are in accordance with the existing theory for an unconfined airflow. Finally, an approximated solution of the critical airflow velocity in terms of the distance is suggested.

中文翻译：

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墙面倒立悬臂板发散不稳定性的数值和实验研究

我们提供了一个数值和实验研究的倒置悬臂板在均匀的轴向亚音速气流中的静态发散不稳定性。假定流动理想，并受刚性通道壁的限制。与传统的板不同，倒置的悬臂板具有夹紧的后缘和自由的前缘。利用有限差分法求解板块运动方程，并将线性边界元方法应用于流体方程。开发了一种新的三角形式涡旋面板模型来解决流体力。针对发散不稳定性开发了一种等效的测试方法，并将其用于实验研究。对于板和刚性通道壁之间的各种距离，评估刚性壁的效果，临界气流速度随着距离的增加而增加。数值计算和预测结果与实验结果吻合良好。当距离足够大时，数值结果与无约束气流的现有理论一致。最后，提出了关于距离的临界气流速度的近似解。