基于复模态方法的二维夹层壁板颤振分析

THE FLUTTER ANALYSIS OF TWO-DIMENSIONAL SANDWICH PANEL BASED ON COMPLEX MODAL METHOD

本文研究二维夹层壁板在一侧受超音速气动力的情况下的颤振现象.利用复模态方法和伽辽金方法分析颤振临界马赫数以及夹芯粘性阻尼对颤振的影响.结果发现考虑前四阶模态时,由于一二阶频率重合而使振动能量积聚发生颤振.考虑中间层的粘弹性时,发现随着粘性阻尼的增加,颤振临界马赫数和临界颤振频率均呈现先降低后升高的现象,其原因是粘弹性一方面降低系统固有频率使得临界马赫数降低,另一方面又使能量耗散使得临界马赫数升高,在这两种作用的影响下出现了上述复杂的现象.本文的研究结果有利于颤振抑制时的设计优化.

The flutter of two-dimensional sandwich panel with supersonic aerodynamic loading on one side is studied. The flutter critical Mach number and the effect of viscous damping are studied by using the Galerkin method and the complex modal method. The results show that the flutter occurs when the first and the second mode natural frequency coalesce, where the vibration energy accumulation starts to be positive. Considering the viscoelasticity of the mid-layer, the results show that with the increase of viscous damping, the critical flutter Mach number and the corresponding critical flutter frequency of the system will decrease at first and then in- crease. It is concluded that the reason for this phenomenon is due to the dual effect of the viscous damping. The viscous damping can reduce the natural frequency to make the system less stable at one hand, and absorb energy which enhances the stability at the other hand. The system appears complex phenomenon as the result of dual effects of the viscous damping. The conclusions of this research will be meaningful in the design of composite panels in supersonic flow.