Dynamics of cantilevered pipes conveying fluid. Part 1: Nonlinear equations of three-dimensional motion

In a three-part study, the first part being this paper, the investigation of the three-dimensional nonlinear dynamics of unrestrained and restrained cantilevered pipes conveying fluid is undertaken. The full derivation of the equations of motion in three dimensions for the plain cantilevered pipe is presented first in this paper, using a modified version of Hamilton's principle, adapted for an open system. Intermediate (between the clamped and free end) nonlinear spring constraints are then incorporated into the equations of motion via the method of virtual work. Furthermore, a point mass fixed at the free end of the pipe is also added to the system. The equations of motion are presented in dimensionless form and then discretized with Galerkin's method.