Two-phase flows are common in large-scale power systems and petroleum industry. During upstream oil and gas productions, crude oil, gas and sand eroded from formation zones are often conveyed as a mixture through horizontal pipes up to the well heads and between well heads and flow stations. In this work, governing equations and boundary conditions (BCs) for the motion of vibrating pipe conveying two phase flow were developed. Hamilton's principle was employed, where the kinetic energies of each phase and of the pipe were combined with the strain energy of the vibrating Euler-Bernoulli pipe. Solutions were presented for vibrating horizontal pipe using Eigenfunction expansion method and Runge Kutta technique. The linear frequencies were obtained for three different boundary conditions (BCs) where parametric analysis is performed to elucidate the effects of initial curvature amplitude, volume fraction and mass ratio. Furthermore, the developed model is used to investigate the effects of these parameters on the dynamic nonlinear behaviour of a pipe conveying two phase flow for vanishing and non-vanishing longitudinal vibrations. The linear analysis shows that as the volume fraction of the sand increases in the two phase flow, the natural frequencies decrease. The initial curvature has similar effect on the vanishing and non-vanishing longitudinal vibrations for all BCs considered. However, increase in volume fraction from low to mid value increases the nonlinear displacement of the pipe after the bifurcation point. Beyond the mid value of volume fraction, the nonlinear displacement reduces. This is absent in pipes conveying single phase flow.

两相流在大型电力系统和石油工业中很常见。在上游油气生产过程中，地层侵蚀的原油、天然气和砂石经常作为混合物通过水平管道输送到井口以及井口与流动站之间。在这项工作中，开发了用于输送两相流的振动管运动的控制方程和边界条件 (BC)。采用汉密尔顿原理，其中每一相和管道的动能与振动的欧拉-伯努利管道的应变能相结合。提出了使用本征函数展开法和龙格库塔技术振动水平管的解决方案。获得了三种不同边界条件 (BC) 的线性频率，其中进行参数分析以阐明初始曲率幅度、体积分数和质量比的影响。此外，开发的模型用于研究这些参数对输送两相流的管道的动态非线性行为的影响，用于消失和不消失的纵向振动. 线性分析表明，随着两相流中沙子的体积分数增加，固有频率降低。对于所有考虑的 BC，初始曲率对消失和不消失的纵向振动具有相似的影响。然而，体积分数从低值到中值的增加会增加分岔点后管道的非线性位移。超过体积分数的中间值，非线性位移减小。这在输送单相流的管道中是不存在的。