固定约束松动对输流管道稳定性和临界流速的影响

把管道固定端抗转动约束松动情况模拟为受扭转弹簧约束的两端支承管道模型，研究了这种输流管道系统在定常内流作用下的稳定性和临界流速，利用两振型Galerkin离散化方法导出了临界流速的解析表达式。用数值方法分析了系统的失稳特性，确定了此系统的首次失稳为静态失稳。利用所导出的临界流速的解析表达式讨论了扭转弹簧刚度、重力系数和轴向力对管道临界流速的影响。

Analysis of critical flow velocities of pipe conveying fluid under relaxation of boundary conditions

The stability and critical flow velocity of a supported pipe conveying fluid are analyzed. The both ends of the pipe are held by the pinned supports with torsional spring constraints. The stability of the fluid-conveying pipe is analyzed using the eigenvalues and eigenfuntions of a beam that has the same boundary conditions as the pipe. Using some numerical method, it is shown that the supported pipe conveying steady flow with the boundary conditions under consideration loses stability first by divergence always. According to the explicit expression derived for the critical flow velocity of the pipe, the effect of some physical parameters of the system, such as the spring constant, gravity and tension, on the values of the critical flow velocity is discussed.