On the Occurrence of Mathieu Instabilities of Vertical Cylinders

Abstract

Large offshore platforms with vertical circular cylindrical hull shapes have been designed and employed in recent times. Classical spar platforms and mono-column concepts are just two examples of designs with such simple configuration, supposed to perform limited motion responses in waves. Reports on investigations on the occurrence of parametric resonance of spar platforms have been published recently in which the relevance of Mathieu amplifications have been assessed making use of different mathematical models. However, some uncertainties still remain on the influence of crucial design parameters as, for instance, metacentric height, draft/diameter ratio, associated damping and mooring system. In an attempt to clarify some of these aspects, in this paper the dynamic stability of a vertical cylinder in regular waves is investigated theoretically and experimentally. A coupled non-linear mathematical model is employed to model and simulate the coupled heave, roll and pitch motions. Theoretical aspects related to the development of resonant motions are discussed. In addition to the numerical and theoretical investigations, an extensive series of experiments with a model of a typical mono-column have been recently conducted at LabOceano. The findings of these investigations are compared and summarized.

Modelling of Parametric Resonance for Heaving Buoys with Position-Varying Waterplane Area

“…This type of parametric resonance in the pitch and/or roll DoFs of floating bodies has been studied since the 19th century, following Froude's observations that large roll motions occur when the roll natural period of a ship is twice the heave or pitch natural period [13]. The parametric coupling between heave, pitch and roll DoFs has been investigated in floating structures, such as ships [14][15][16][17][18] and spars [19][20][21][22][23]. The large amplitude oscillations resulting from parametric resonance can jeopardise the safe operation of floating structures and vessels, such as cargo being lost overboard due to large parametric roll motions on container ships.…”

Parametric excitation suppression in a floating cylinder via dynamic vibration absorbers: a comparative analysis

“…Dynamic instability in floating bodies can occur due to the parametric excitation of the pitch and roll degreesof-freedom (DoFs). This phenomena was first noted by Froude in the nineteenth century [1], and has since been investigated in applications such as shipping [2][3][4], offshore spar-type structures [5][6][7][8] and wave energy converters [9].…”

Opening the air‐chamber of an oscillating water column spar buoy wave energy converter to avoid parametric resonance

“…An oscillating water column (OWC) spar buoy, is a type of wave energy converter (WEC) that utilises the relative heave motion between an outer spar hull and an inner moon poollike water column to drive the air, enclosed in a chamber above the OWC, through a turbine installed at the top of the buoy and connected to the atmosphere. Like many offshore spar structures [1][2][3][4], this device is prone to large amplitude pitch and roll motions, caused by parametric resonance, when the frequency of the waves is around twice the pitch/roll natural frequency, see Figure 1. Parametric resonance is a dynamic instability caused by the time-varying changes in the parameters of a system [5], which manifests in floating offshore structures, due to the wave-induced heave motion of the structure varying the metacentric height.…”