The objective of this paper is to investigate the dynamic instability of deepwater top-tensioned risers (TTRs), when subjected to the fluctuating axial tension originated from the heave motion of a surface floating platform as the instability source. Based on a rigorous derivation on the governing equation, a reduced model of the lateral displacement of a TTR is achieved by an ordinary differential equation with periodic coefficients. To identify the instability range of practical amplitudes and frequencies of the excitation, a newly proposed extended precise integration method (EPIM) is employed to generate the Floquet transition matrix (FTM). EPIM possesses high precision and efficiency due to the doubling algorithm and the increment-storing technique. The instability charts of TTRs in several typical depths are numerically obtained using EPIM. The effects of factors such as the top tension ratio, the stiffness of the heave compensators, damping constant, and internal flow velocity on the instability region are analyzed. In addition, because the nonlinear hydrodynamic damping will lead the TTR’s lateral vibration to reach a steady state, the instability response is thereby simulated by EPIM. Three response scenarios are discussed with examples. As the heave amplitude increases, the parametric resonance of the TTR is first triggered, then the transition stage appears, and ultimately the local dynamic buckling occurs. The bending stress analysis shows that the local dynamic buckling is the worst scenario for structural safety.
Consolidation analysis of transversely isotropic layered saturated soils in the Cartesian coordinate system by extended precise integration method
