Experimental Analysis of a Vertical and Flexible Cylinder in Water: Response to Top Motion Excitation and Parametric Resonance

Abstract

Experiments with a vertical, flexible, and submerged cylinder were carried out to investigate fundamental aspects of risers dynamics subjected to harmonic excitation at the top. The flexible model was designed aiming a high level of dynamic similarity with a real riser. Vertical motion, with amplitude of 1% of the unstretched length, was imposed with a device driven by a servomotor. Responses to distinct exciting frequency ratios were investigated, namely, ft:fN,1 = 1:3; 1:1; 2:1, and 3:1. Cartesian coordinates of 43 monitored points positioned all along the span were experimentally acquired by using an optical tracking system. A simple Galerkin's projection applied for modal decomposition, combined with standard Mathieu chart analysis, led to the identification of parametric resonances. A curious finding is that the Mathieu instability may simultaneously occur in more than one mode, leading to interesting dynamic behaviors, also revealed through standard power spectra analysis and displacement scalograms.

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

“…First, classic parametric resonance may develop when the frequency and amplitude of the floater's heave excite a specific riser mode or combination of modes. In this situation, the response frequency is about twice the excited eigen-frequency (Park and Jung, 2002), also as confirmed by experiments (Franzini et al, 2015). Second, sub-critical buckling can arise when the floater heaves with low frequency and large amplitude, and thus a single wave grows near the riser's bottom and then propagates along its length.…”

“…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).…”

“…A couple of experiments have been reported in the literature. The first one (Franzini et al, 2015) used spectral analysis of the experiments and Strutt diagrams to investigate the response at different frequency ratios of top excitation to eigen frequency. The second (Mazzilli et al, 2016) used the Galerkin method with Bessel functions to solve the riser's motion numerically and compared the results against experimental data.…”

Coupled Vibration Analysis of Submerged Floating Tunnel System in Wave and Current

“…Compared with the tunnel tube, oscillation of the SFT cables in fluid flow is more prone to occurring due to the periodic vortex shedding, known as vortex-induced vibration (VIV) [12]. Furthermore, because the top end of the anchor-cable is connected to the tube body, similar to other top-tensioned risers (TTR) in deep water platforms, the cables simultaneously encounter parametric excitations due to the time-varying tension which results from the motions of SFT tube under the environmental loads (such as regular waves) [13][14][15]. Hence, the local dynamic behavior of the cables is always a key problem in the design stage.…”

“…They also studied the effects of parametric resonance on the tension forces of the vertical tethers in ABAQUS. Meanwhile, more research has been directed toward the dynamics of TTR under combined vortex and parametric excitations by means of FEM, semi-empirical models [13,14] and experimental investigations [15].…”