输流粘弹性曲管的稳定性分析

根据变质量弹性系统Hamilton原理，用变分法建立了输流粘弹性曲管的运动微分方程，并用归一化幂级数法导出了输流粘弹性曲管的复特征方程组．以两端固支Kelvin-Voigt模型粘弹性输流圆管为例，分析了无量纲延滞时间和质量比对输流管道无量纲复频率和无量纲流速之间的变化关系的影响．在无量纲延滞时间较大时，粘弹性输流圆管的特点是它的第1、2、3阶模态不再耦合，而是在第1、第2阶上先发散失稳，然后在1阶模态上再发生单一模态颤振．

Stability Analysis of Viscoelastic Curved Pipes Conveying Fluid

Based on the Hamilton's principle for elastic systems of changing mass, a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method, and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method. The effects of dimensionless delay time on the variation relationship between dimensionless complex frequency of the clamped_clamped viscoelastic circular pipe conveying fluid with the Kelvin_Voigt model and dimensionless flow velocity were analyzed. For greater dimensionless delay time, the behavior of the viscoelastic pipe is that the first, second and third mode does not couple, while the pipe behaves divergent instability in the first and second order mode, then single_mode flutter takes place in the first order mode.