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 p...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11902112,11972167,and 12072119)Hubei Superior and Distinctive Discipline Group of"Mechatronics and Automobiles"(Grant No.XKQ2021042).
文摘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.
