基于薄板小挠度理论和Kelvin-Voigt黏弹性本构方程，建立了轴向运动黏弹性夹层板横向振动控制方程，研究了其横向振动特性。采用一阶和二阶Galerkin截断得到夹层板横向振动的特征方程，讨论了两种夹心层所占总厚度比率下轴向运动速度对其横向振动特性的影响。研究表明：在未超过临界速度前，无论一阶还是二阶截断，在定性描述系统特征上二者相同，但一阶截断不适合描述轴向运动速度超过临界速度的情形；对四边简支黏弹性夹层板，临界速度和发生耦合模态颤振的速度随着夹心层比率的减少逐渐增大。
Based on the theory of small deflection of thin plate and the constitutive description of Kelvin-Viogt viscoelastic material, the controlling equation which dominates the transverse vibration of the axially moving viscoelastic sandwich plate was established, followed by the study of the transverse vibration characteristic. One- mode and two-mode eigenequation were obtained by using 1-term and 2-term Galerkin truncation. The influence of the ratio of the core and axially moving velocity on the transverse vibration characteristic was discussed. It is found that both 1-term and 2-term Galerkin truncation results fit well when the axially moving velocity doesnrt exceed the critical velocity. However, 1- term Galerkin truncation will not suit any more when the axially moving velocity exceeds the critical velocity. For simply supported plate at four sides, the critical velocity and coupled mode flutter velocity increase with the decrease of ratio of core.
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