简支Mexwell模型粘弹性输流管道的稳定性分析

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。

Stability Analysis of Maxwell Viscoelastic Pipes ConveyingFluid With Both Ends Simply Supported

On the basis of some studies of elastic pipe conveying fluid, the dynamic behavior and stability of Maxwell viscoelastic pipes conveying fluid with both ends simply supported, which are gyroscopic conservative system, were investigated by using the finite difference method and the corresponding recurrence formula. The effect of relaxation time of viscoelastic materials on the variation curve between dimensionless flow velocity and the real part and imaginary part of dimensionless complex frequencies in the first three order modes were analyzed concretely. It is found that critical flow velocities of divergence instability of Maxwell viscoelastic pipes conveying fluid with both ends simply supported decrease with the decrease of the relaxation time, while after the onset of divergence instability (buckling) critical flow velocities of coupled_mode flutter increase with the decrease of the relaxation time. Particularly, in the case of greater mass ratio, with the decrease of relaxation time, the onset of coupled_mode flutter delays, and even does not take place. When the relaxation time is greater than 10 3, stability behavior of viscoelastic pipes conveying fluid is almost similar to the elastic pipes conveying fluid.