Dynamic modeling of mass-flowing linear medium with large amplitude displacement and rotation

In this paper, a dynamic model of a linear medium with mass flow, such as traveling strings, cables, belts, beams or pipes conveying fluids, is proposed, in the framework of Arbitrary-Lagrange–Euler (ALE) description. The material coordinate is introduced to characterize the mass-flow of the medium, and the Absolute Nodal Coordinate Formulation (ANCF) is employed to capture geometric nonlinearity of the linear media under large displacement and rotation. The governing equations are derived in terms of dʹAlembertʹs principle. When using an ALE description, complex mass-flowing boundary conditions can be easily enforced. Numerical examples are presented to validate the proposed method by comparison with analytical results of simplified models. The computed critical fluid velocity for the stability of a cantilevered pipe conveying fluid is correlated with the available theory in literature. The large amplitude limit-cycle oscillations of flexible pipes conveying fluid are presented, and the effect of the velocity of the fluid on the static equilibrium of the pipe under gravity is investigated.