Abstract A geometrically-exact nonlinear theory is developed for pipes conveying fluid based on the total momentum of the fluid and pipe. The proposed model accounts for geometric and kinematic nonlinearities of the pipe and inertial coupling between the pipe and internal flow. The fully nonlinear differential governing equations are derived based on the momentum balance of pipe and fluid in floating non-inertial frames, allowing for large displacements and overall rigid-body motions. The internal fluid pressures along a pipe are considered; the fluid is viscous but assumed to be incompressible and homogeneous. A separation of displacements technique combined with an assumption of small incremental displacements is used to derive an updated Lagrangian formulation, which allows a large-displacement nonlinear model to be converted into a series of piecewise-linear models. The resulting time-stepping method is numerically implemented using the finite-volume discretization. The effectiveness of the proposed developments is demonstrated in a series of numerical examples, including a cantilever pipe discharging fluid, a semi-circular curved pipe, and a marine riser subject to top tension and forced motion. The new model is shown to predict an unstable flutter at a relatively low flow velocity for a cantilever discharging pipe, and to predict a transition behavior before the onset of the observed flutter instability.

中文翻译：

---

基于几何精确动量的管道输送流体非线性理论

摘要 基于流体和管道的总动量，发展了一种几何精确非线性理论，用于输送流体的管道。所提出的模型考虑了管道的几何和运动非线性以及管道与内部流动之间的惯性耦合。完全非线性微分控制方程是基于浮动非惯性框架中管道和流体的动量平衡推导出来的，允许大位移和整体刚体运动。考虑沿管道的内部流体压力；流体是粘性的，但假定为不可压缩且均质的。位移分离技术与小增量位移假设相结合，用于推导出更新的拉格朗日公式，它允许将大位移非线性模型转换为一系列分段线性模型。由此产生的时间步长方法是使用有限体积离散化在数值上实现的。所提议的开发的有效性在一系列数值例子中得到证明，包括排放流体的悬臂管、半圆形弯管和承受顶部张力和受迫运动的海洋立管。新模型可以预测悬臂排放管在相对低流速下的不稳定颤振，并在观察到的颤振不稳定开始之前预测过渡行为。所提议的开发的有效性在一系列数值例子中得到了证明，包括排放流体的悬臂管、半圆形弯管和承受顶部张力和受迫运动的海洋立管。新模型可以预测悬臂排放管在相对低流速下的不稳定颤振，并在观察到的颤振不稳定开始之前预测过渡行为。所提议的开发的有效性在一系列数值例子中得到了证明，包括排放流体的悬臂管、半圆形弯管和承受顶部张力和受迫运动的海洋立管。新模型可以预测悬臂排放管在相对低流速下的不稳定颤振，并在观察到的颤振不稳定开始之前预测过渡行为。