Non-smooth dynamics of articulated pipe conveying fluid subjected to a one-sided rigid stop

摘要

The mathematical model and non-smooth dynamics of a two-segment articulated pipe conveying fluid with the upper segment subjected to a one-sided rigid stop is investigated. To determine the effect of the one-sided rigid stop on the impacting behaviors of the articulated pipe under various geometrical and physical parameters, the nonlinear equations of motion combined with the rigid impacting condition are established and solved by a fourth-order Runge-Kutta algorithm. In the linear analysis, the stabilities and critical flow velocities of the articulated pipe are analyzed by examining the linearized equations without the rigid stop. Typical results of stability boundaries are compared to those reported previously and good agreement is obtained. In the nonlinear analysis, bifurcation diagrams and phase portraits of the responses of the upper and lower segments are presented and discussed by considering the effects of mass ratio, stiffness ratio, stop gap and coefficient of restitution. Periodic and chaotic vibro-impact oscillations are observed, with a particular interest in the detecting of the possibility of stick-slip motions which show the non-smooth vibrating characteristics of this rigid impacting system. It is shown that the coefficient of restitution for impact has a great effect on the chaotic oscillations and stick-slip motions of the pipe. Results obtained in this work highlight the complexity of the nonlinear impacting dynamics of articulated pipes conveying fluid with a rigid stop. It is also expected, in the near future, to extend the basic idea of this work to explore the nonlinear responses of flexible pipes and hoses conveying fluid subjected rigid stops by introducing a multi-segment articulated pipe model.