Vibrations in 3D space of a spinning supported pipe exposed to internal and external annular flows

This paper conducts a dynamical analysis of drill-string-like pipes based on the ground-breaking contribution of Païdoussis et al. (2008), in which the stability of a tubular cantilever conveying internal and external annular flows without spin is investigated. The innovations of this paper are generalized as follows: i) A spinning three-dimensional (3D) model is developed to simulate working drill strings; ii) Supported pipes instead of cantilevers are considered due to the stabilizers and heavy loads encountered at the free end (the drill bit); iii) Hamiltonian, instead of Newtonian, derivation is performed to achieve the governing equations of such system with gyroscopic effects induced by spinning motion and fluid–structure interaction (FSI), namely a doubly gyroscopic system; iv) 3D motions, involving in-plane and out-of-plane transverse motions, are studied; v) The frequencies, energy, mode shapes and time-domain responses to the initial conditions are comprehensively investigated to display the dynamical characteristics of the system. The results obtained reveal that the viscous external fluid, flow velocity, spinning speed as well as the gravity and axial pretension all have significant effects on the dynamical behaviors of the pipe. The dynamics of the present system has been demonstrated rather different from that of cantilevered structures without spin.