A combined energy method is proposed to investigate the flutter instability characteristics of weakly damped panels in the supersonic airflow. Based on the small damping assumption, the motion governing partial differential equation (PDE) of the panel aeroelastic system, is built by adopting the first-order piston theory and von Karman large deflection plate theory. Then by applying the Galerkin procedure, the PDE is discretized into a set of coupled ordinary differential equations, and the system reduced order model (ROM) with two degrees of freedom is obtained. Considering that the panel aeroelastic system is non-conservative in the physical nature, and assuming that the panel exhibits a single period oscillation on the flutter occurrence, the non-conservative energy balance principle is applied to the linearized ROM within one single oscillation period. The obtained result shows that the ROM modal coordinate amplitudes ratio is regulated by the modal damping coefficients ratio, though each modal damping coefficient is small. Furthermore, as the total damping dissipation energy can be eliminated due to its smallness, the He’s energy balance method is applied to the undamped ROM, therefore the critical non-dimensional dynamic pressure on the flutter instability occurrence, and the oscillation circular frequency amplitude relationship (linear and nonlinear form) are derived. In addition, the damping destabilization paradoxical influence on the system flutter instability is investigated. The accuracy and efficiency of the proposed method are validated by comparing the results with that obtained by using Routh Hurwitz criteria.

中文翻译：

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超声速气流中弱阻尼面板颤振不稳定性分析的组合能量法

提出了一种组合能量方法来研究超声速气流中弱阻尼板的颤振失稳特性。基于小阻尼假设，采用一阶活塞理论和冯·卡曼大挠度板理论，建立了面板气动弹性系统的运动控制偏微分方程（PDE）。然后通过应用Galerkin程序，将PDE离散化为一组耦合的常微分方程，并获得具有两个自由度的系统降阶模型（ROM）。考虑到面板的空气弹性系统在物理性质上是非保守的，并假设面板在颤振发生时表现出单周期振荡，在一个单一的振荡周期内将非保守的能量平衡原理应用于线性化ROM。所得结果表明，尽管各模态阻尼系数很小，但ROM模态坐标幅值比是由模态阻尼系数比来调节的。此外，由于可以减小总阻尼耗散能量，因为它的体积很小，因此将He的能量平衡方法应用于无阻尼ROM，因此对颤振不稳定性产生了临界的无量纲动压力，并且振荡圆频率振幅关系（线性和非线性形式）。此外，研究了阻尼不稳定对系统颤振不稳定性的反常影响。