This paper focuses on the derivation of the aerodynamic force for the cantilever plate in subsonic flow. For the first time, a new analytical expression of the quasi-steady aerodynamic force related to the velocity and the deformation for the high-aspect-ratio cantilever plate in subsonic flow is derived by utilizing the subsonic thin airfoil theory and Kutta-Joukowski theory. Results show that aerodynamic force distribution obtained theoretically is consistent with that calculated by ANSYS FLUENT. Based on the first-order shear deformation and von Karman nonlinear geometric relationship, nonlinear partial differential dynamical equations of the high-aspect-ratio plate subjected to the aerodynamic force are established by using Hamilton’s principle. Galerkin approach is applied to discretize the governing equations to ordinary differential equations. Numerical simulation is utilized to investigate the relation between the critical flutter velocity and some parameters of the system. Results show that when the inflow velocity reaches the critical value, limit cycle oscillation occurs. The aspect ratio, the thickness, and the air damping have significant impact on the critical flutter velocity of the thin plate.

中文翻译：

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高音速比悬臂板在亚音速流中的新型气动力和颤振

本文着重于亚音速流中悬臂板空气动力的推导。首次利用亚音速薄翼型理论和Kutta-Joukowski理论推导了与高速比悬臂板在亚音速流中的速度和变形有关的准稳态空气动力的新解析表达式。结果表明，理论上获得的空气动力分配与ANSYS FLUENT计算的一致。基于一阶剪切变形和von Karman非线性几何关系，利用汉密尔顿原理建立了高纵横比板受到空气动力的非线性偏微分动力学方程。应用Galerkin方法将控制方程离散为常微分方程。利用数值模拟研究了临界颤振速度与系统某些参数之间的关系。结果表明，当流入速度达到临界值时，就会出现极限循环振荡。长宽比，厚度和空气阻尼对薄板的临界颤动速度有重要影响。