Dynamic stability of a stepped drillstring conveying drilling fluid

Taking into account differences between a drill pipe (DP) and a drill collar (DC), the drillstring
in a vertical well is modeled as a stepped pipe conveying a drilling fluid downwards
to the bottom inside the string and then upwards to the ground from the annulus. An analytical
model that describes lateral vibration of the drillstring and involves the drillstring
gravity, weight on bit (WOB), hydrodynamic force and damping force of the drilling fluid
is established. By analysis of complex frequencies, the influences of WOB, borehole diameter,
DP length, velocity and density of the drilling fluid on the stability of the system are
discussed.