The present work is devoted to providing a full version of theoretical model for three-dimensional (3D) oscillations of a cantilevered pipe conveying fluid under large deformation. The geometric nonlinearity of the pipe is exactly considered by using an exact expression for the curvature of the pipe centerline. By taking variation operations with translational displacements or bending angles as the variables, two types of geometrically exact (GE) governing equations are derived and they are demonstrated to be equivalent. By using Taylor expansion (TE), the derived GE equations can degenerate into the previous version of governing equations based on a small-amplitude assumption. Analyses of the stability and nonlinear vibrations are conducted by means of both GE and TE models. As expected, the results of the pipe’s stability and small-amplitude oscillations predicted by using the TE model agree well with the counterpart predicted by the GE model. When the vibration amplitude of the pipe becomes large, however, remarkable difference can be found between the results obtained by using the TE and GE models. Besides, in some cases, the large-amplitude oscillations of the pipe predicted by the TE model may be unrealistic. Therefore, the newly developed GE model is more reliable for evaluating the 3D motions of cantilevered pipes conveying fluid under large deformation.

目前的工作致力于为悬臂式管道输送大变形流体的三维 (3D) 振荡提供完整版本的理论模型。通过使用管道中心线曲率的精确表达式，可以准确地考虑管道的几何非线性。通过以平移位移或弯曲角为变量的变分运算，推导出两类几何精确（GE）控制方程，并证明它们是等价的。通过使用泰勒展开 (TE)，导出的 GE 方程可以退化为基于小幅度假设的先前版本的控制方程。稳定性和非线性振动的分析是通过 GE 和 TE 模型进行的。正如预期的那样，TE模型预测的管道稳定性和小幅振荡结果与GE模型预测的结果吻合较好。但是，当管道的振动幅度变大时，可以发现使用 TE 和 GE 模型获得的结果之间存在显着差异。此外，在某些情况下，TE 模型预测的管道大振幅振荡可能不切实际。因此，新开发的GE模型对于评估大变形下输送流体的悬臂管的3D运动更加可靠。在某些情况下，TE 模型预测的管道大振幅振荡可能不切实际。因此，新开发的GE模型对于评估大变形下输送流体的悬臂管的3D运动更加可靠。在某些情况下，TE 模型预测的管道大振幅振荡可能不切实际。因此，新开发的GE模型对于评估大变形下输送流体的悬臂管的3D运动更加可靠。