基于经典的超音速气流下二维薄壁板颤振控制方程, 采用kelwin粘弹性模型将阻尼引入到方程中。通过假设模态和Garlerkin方法将方程离散化, 推导出气动弹性系统的状态方程;通过求解状态方程中矩阵的特征值问题确定壁板的颤振临界点。分析了粘弹性阻尼对颤振特性的影响。结果表明, 当粘弹性阻尼不大时(欠阻尼)颤振临界动压较无阻尼时小, 且阻尼越大, 临界动压越小;当粘弹性阻尼较大时(过阻尼以后)临界动压先是随阻尼增大而减小, 后随阻尼的增大而增大, 发生具有明显振动特征的某两阶模态相关的单模态颤振, 颤振临界模态是两者中的前一阶。阻尼增大到一定程度后可推迟颤振的发生, 从理论上为将大阻尼粘弹性材料用于飞行器壁板的颤振被动控制上提供一定参考价值。

In this paper, based on the partial differential governing equation of isotropic flat panel in classic supersonic flow, the viscoelastic structural damping is introduced into the equation by using Kelvin′s model.Dynamic instability behavior of a linear viscoelastic panel in supersonic flow is investigated.The quasi-steady piston theory of supersonic flow is employed under the aerodynamic pressure.The panel governing equation is transformed into a set of ordinary differential equations via the Galerkin approach.First-order state equations are then obtained and solved by means of a standard eigenvalue calculation.The dynamic instability of viscoelstic panels is predicted by the feature of characteristic roots.The phenomena of coupled-mode flutter without structural damping and single-mode flutter with structural damping induced by the supersonic flow are observed for the different dynamic pressure values.Results indicate that structural damping plays an important role in the stability of panels flutter.Sufficient damping can remarkably defer the flutter threshold.