在弹性输流管道研究的基础上 ,采用递推格式的有限差分法 ,对简支Maxwell模型粘弹性输流管道 (回转守恒系统 ) ,探讨了其动力特性和稳定性问题 ,具体分析了材料的松弛时间对无量纲流速与前三阶模态的无量纲频率的实部及虚部之间的变化曲线的影响·　发现发散临界流速随松弛时间的减小而降低 ,随后发生的耦合模态颤振临界流速随松弛时间的减小而增大 ;甚至在质量比较大时 ,随着松弛时间的减小 ,可推迟乃至不发生耦合模态颤振·　当无量纲松弛时间达到 10 3量级以上时 ,即可将其按弹性管道处理·　甚至在 H为 10 2 量级时 ,按弹性管道处理也不会带来太大的误差 Based on the research of elastic fluid-conveying pipe, the finite difference method of recursive finite element method is used to investigate the dynamic characteristics and stability of simple-supported Maxwell model viscoelastic fluid-conveying pipe (rotating conservation system) The Effect of Relaxation Time on the Variation between the Real and Imaginary Parts of the Dimensionless Flow Rate and the Dimensionless Frequency of the First Third Order Mode The critical flow rate of divergence is found to decrease as the relaxation time decreases and the resulting coupled modal flutter Vibrational critical flow rate increases with decreasing relaxation time, and even with large mass, coupled mode chattering can be delayed or even absent as the relaxation time decreases. When the dimensionless relaxation time reaches above 10 3 level , It can be treated as flexible pipe. Even when H is 10 2, it will not bring too much error by elastic pipe treatment