Parametric instability analysis of deepwater top-tensioned risers considering variable tension along the length

Abstract

Parametric instability of a riser is caused by fluctuation of its tension in time due to the heave motion of floating platform. Many studies have tackled the problem of parametric instability of a riser with constant tension. However, tension in the riser actually varies linearly from the top to the bottom due to the effect of gravity. This paper presents the parametric instability analysis of deepwater top-tensioned risers (TTR) considering the linearly varying tension along the length. Firstly, the governing equation of transverse motion of TTR under parametric excitation is established. This equation is reduced to a system of ordinary differential equations by using the Galerkin method. Then the parametric instability of TTR for three calculation models are investigated by applying the Floquet theory. The results show that the natural frequencies of TTR with variable tension are evidently reduced, the parametric instability zones are significantly increased and the maximum allowable amplitude of platform heave is much smaller under the same damping; The nodes and antinodes of mode shape are no longer uniformly distributed along the axial direction and the amplitude also changes with depth, which leads to coupling between the modes. The combination resonance phenomenon occurs as a result of mode coupling, which causes more serious damage.

Vortex-Induced Vibration Response Bifurcation Analysis of Top-Tensioned Riser Based on the Model of Variable Lift Coefficient

“…Thus, TTR can be modeled as a simply supported beam with top tension. Assume the VIV caused by the current; the schematic diagram and simplified force diagram of the TTR are shown in Figures 1(a) and 1(b), respectively [8][9][10].…”

Numerical and Experimental Research on the Effect of Platform Heave Motion on Vortex‐Induced Vibration of Deep Sea Top‐Tensioned Riser

“…Equation (2) shows that the effective tension in riser has static and dynamic components. e static component of the tension comes from the pretension imposed by the heave e dynamic component of the tension is caused by the heaving platform, and (Ω,a) is generally referred to as parametric excitations for the transverse vibration of TTR [21,22]. erefore, equation ( 1) is a partial differential equation with periodic variable coefficient, and this is different from the partial differential equation with constant variable coefficient in [23].…”

“…e number of active modes was found to be strongly dependent on the period of the riser tension. Although this fluctuation tension is generally significantly reduced by heave compensators, it still might destabilize the straight equilibrium of the riser and cause it to vibrate at a dangerously high level [21,22].…”

Long-term stochastic heave-induced dynamic buckling of a top-tensioned riser and its influence on the ultimate limit state reliability

“…Many studies have been devoted to the issue of parametric excitation of offshore structures in which a coefficient appears as function of time in the governing differential equation. Said studies have included the research about risers and cables (Chatjigeorgiou, 2004;Chatjigeorgiou andMavrakos, 2005, 2002;Franzini et al, 2015;Franzini and Mazzilli, 2016;Hsu, 1975;Kuiper et al, 2008;Lei et al, 2014;Park and Jung, 2002;Prado et al, 2014;Wang et al, 2015;Wu et al, 2016;Xiao and Yang, 2014;Yang et al, 2013;Yang and Xiao, 2014;Zhang and Tang, 2015), tethers for tension-leg platforms Park, 1995, 1991), submerged floating pipelines (Yang et al, 2017) and parametric rolling of ships (Pipchenko, 2009;Thomas et al, 2010).…”

“…(2.a) Then the stability of the linear Mathieu's equation (for single-frequency excitation) (Chatjigeorgiou and Mavrakos, 2002;Hsu, 1975;Park and Jung, 2002;Park, 1995, 1991;Prado et al, 2014;Wang et al, 2015) or Hill's equation (for multi-frequency excitation) (Xiao and Yang, 2014;Yang et al, 2013) is analyzed via the Strutt's diagram, where the stability is estimated analytically. (2.b) Another alternative is to analyze the linearized system by means of the Floquet theory (Kuiper et al, 2008;Lei et al, 2014;Zhang and Tang, 2015). (3) Finally, the nonlinear equation is solved in the time-domain to examine the effect of nonlinear terms (Chatjigeorgiou and Mavrakos, 2002) and the map of the steady-state amplitude can be plotted (Franzini and Mazzilli, 2016;Kuiper et al, 2008;Mazzilli et al, 2016;Prado et al, 2014).…”