Dynamic analysis of an axially moving underwater pipe conveying pulsating fluid

Abstract

In this paper, both linear and non-linear dynamics of a slender and uniform pipe conveying pulsating fluid, which is axially moving in an incompressible fluid, are comprehensively studied. The vibration equations of the system are established by considering various factors, including a coordinate conversion system, an “axial added mass coefficient” describing the additional inertia forces caused by the external fluid, the Kelvin–Voigt viscoelastic damping, a kind of non-linear additional axial tension, and the pulsating internal fluid. The vibration equations are discretized by the Galerkin procedure and solved by the Runge–Kutta approach, and the validity of the solution procedure is carefully checked. After that, the linear and non-linear responses of the system are studied when the internal flow velocity and the axially moving speed of the pipe are small. For linear responses, the Kelvin–Voigt viscoelastic damping has great influences on the second and third modes of the system. For the non-linear dynamic, the results are rich and changeful, including the first and second principal parametric resonances, the secondary resonance, the combination resonance, period-1 motion, quasi-periodic motion, and chaotic motion. Finally, the influence of several key system parameters on the non-linear responses is analyzed.

Analytical Studies of Fluid Conveying Pipes on Viscoelastic Foundation Using Differential Transforms Method

“…Over the past 60 years, researchers have investigated the stability and vibration of pipelines that convey fluids using both theoretical and experimental methods. An excellent assessment was given in the literature [1][2], even while most of the study focus on pipes carrying fluid which however have produced significant rewards, including; (i) the creation of theories for particular types of dynamic systems and novel analytical techniques for these systems; (ii) the knowledge of dynamics in more complicated systems (for instance, analyzing the dynamics and solidity of bent and twisted pipes that convey fluid in various spatial shapes), then (iii) the immediate implementation of this analysis in certain unforeseeable practical functions in the past. An essential step in the design process is the investigation of a pipeline's stability and vibration.…”