中文摘要：

对超音速来流中的四边简支粘弹性夹层壁板颤振问题进行了研究。基于Kelvin—Voigt粘弹性本构模型、小变形理论和一阶气动力活塞理论建立了三维粘弹性夹层壁板的气动弹性颤振方程。使用Galerkin方法将粘弹性夹层壁板气动力方程简化，并使用数值方法进行求解。讨论了粘弹性阻尼、来流动压和夹心层厚度对颤振特性的影响。研究表明：（1）随着来流动压的增大，系统一阶频率增大，二阶频率减少，一阶频率和二阶频率相等后，系统阻尼变为两个分支，系统某一分支阻尼为零时，系统发生颤振，此时来流动压为颤振临界动压。（2）随着粘弹性阻尼系数的增大，系统的频率有所减小，但影响远不及夹心层占总厚度比值的影响大。（3）随着夹心层厚度的增大，系统的临界颤振动压减小。

英文摘要：

Flutter problems of the viscoelastic sandwich panel under supersonic speed are presented. Based on the theory of small deflection of thin panel, the governing equation which dominates the flutter vibra- tion of the viscoelastic sandwich panel is established taking into account the constitutive description of Kelvin-Voigt viscoelastic material and linear piston theory. Discrete ordinary equations are obtained by u- sing Galerkin truncation method and solved by using numerical simulation method. The influence of visco- elastic damping coefficient dynamic pressure and thickness of core layer on the fluttering characteristic are discussed. It is found that. （1） Along with the increase of dynamic pressure, the primary circular fre- quency increases, second circular frequency decreases. Once they equal each other, aerodynamic damping becomes two branches, the fluttering phenomenon occurs when one branch of the aerodynamic damping e- quals zero. （2）Along with the increase of viscoelastic damping coefficient, frequency of sandwich panel decrease slightly. Compared with the ratio of core layer, the former＇s influence on the system is far from the latter. （3）With the increase of ratio of core layer, critical flutter dynamic pressure decreases.