Bifurcation Analysis and Vibration Control of a Top-Tensioned Riser Under Parametric Resonance with a Tuned Mass Damper

This paper presents a dynamic model of a top-tensioned riser (TTR) subjected to combined vortex-induced vibration (VIV) and time-varying tension excitation. The model employs a van der Pol oscillator to simulate load excitation caused by vortex shedding and incorporates a tuned mass damper (TMD) to suppress nonlinear vibrations in the riser. The key contributions include, first, employing the Galerkin method to obtain a multi-mode approximate solution and analyzing it using single-mode approximate equations, and subsequently, applying a multi-scale approach to investigate the vibration reduction effect of the TMD under two typical resonance scenarios. By introducing a complex impedance term derived from the complex transfer function, the physical effect of the TMD is transformed into a frequency-dependent dynamic reaction force coupled to the riser’s equation of motion. The first involves 1:1 internal resonance between the structural frequency and vortex-induced frequency, while the second involves 1:2 parametric resonance between the structural frequency and the top tension frequency. Results indicate that when the structural frequency exhibits 1:2 parametric resonance with the top tension frequency, complex bifurcation behavior occurs, leading to large-amplitude structural responses. Findings demonstrate that TMDs effectively alter the system’s stability distribution and exhibit outstanding vibration-reduction efficiency under both typical resonance conditions.