刚柔混杂输流管的稳定性研究

Stability analysis of a hybrid flexible-rigid pipe conveying fluid

性输流管和铰接刚性输流管的稳定性和动力学问题备受流固耦合领域研究人员的关注.弹性管和刚性管串联而成的混杂输流管是典型的刚柔耦合系统.基于Hamilton原理,建立了由悬臂弹性管、转动弹簧和刚性管依次串联而成的刚柔混杂输流管的控制方程,并采用伽辽金法对控制方程进行离散化.本文通过将混杂输流管的结构参数极端化来逼近典型的弹性输流管,验证了数学模型的合理性.理论研究中,计算了混杂输流管系统的临界流速随转动弹簧刚度、质量比和长度比的变化规律.从特征值的演化趋势中识别了混杂输流管系统首次发生失稳的模态阶次,并与弹性输流管的失稳形式进行了对比分析.数值结果表明,结构参数对刚柔混杂输流管系统的临界流速有较大影响.转动弹簧刚度值较小时,刚柔混杂输流管更容易发生高阶模态失稳,而较大的刚度值则会引起二阶模态失稳.在特定的结构参数范围内,随着流速的增加,刚柔混杂管道还可能发生失稳模态的跃迁.取某些结构参数时,刚柔混杂输流管系统还可能首先发生四阶模态失稳.本文的研究结果有助于理解和控制刚柔混杂输流管的动力学问题.

The stability and dynamical behavior of flexible and articulated rigid pipes conveying fluid have attracted the attention of many researchers in the field of fluid-structure interactions.The system of an articulated pipe composed of a flexible pipe and a rigid pipe is a class of hybrid flexible-rigid dynamical problems involving flow-induced vibrations.This paper establishes the governing equations of motion of a hybrid flexible-rigid pipe system based on Hamilton's principle,with the rigid pipe being hinged to the lower end of a flexible cantilevered pipe via a rotational spring.The coupling equations of motion are discretized via a Galerkin's approach.The mathematical model is validated by comparing the eigenvalue branches of a degenerated system by choosing extreme values of the parameters of the hybrid pipe with previous results.In the theoretical analysis,the critical flow velocities are calculated as a function of the stiffness of the rotational spring,mass ratio and length ratio of the rigid and flexible pipes.The unstable modes are detected from the eigenvalue branches and compared with those of a flexible cantilevered pipe.Numerical results show that the critical flow velocity is greatly influenced by several structural parameters.It is found that a small stiffness of the rotational spring tends to predict higher-mode instability,whereas a large rotational spring stiffness would generate a second-mode instability in most cases.In several system parameter spaces,the hybrid pipe may experience a transference of unstable modes with the increase of flow velocity.It is also shown that the hybrid pipe system may lose stability first in the fourth mode in some cases.Some of the fresh results obtained for the hybrid pipe system are expected to be helpful in understanding and controlling the dynamical responses of hybrid flexible-rigid fluid-conveying pipes.