Nonlinear Dynamic and Kinematic Model of a Spar-Buoy: Parametric Resonance and Yaw Numerical Instability

Abstract

<jats:p>Mathematical models are essential for the design and control of offshore systems, to simulate the fluid–structure interactions and predict the motions and the structural loads. In the development and derivation of the models, simplifying assumptions are normally required, usually implying linear kinematics and hydrodynamics. However, while the assumption of linear, small amplitude motion fits traditional offshore problems, in normal operational conditions (it is desirable to stabilize ships, boats, and offshore platforms), large motion and potential dynamic instability may arise (e.g., harsh sea conditions). Furthermore, such nonlinearities are particularly evident in wave energy converters, as large motions are expected (and desired) to enhance power extraction. The inadequacy of linear models has led to an increasing number of publications and codes implementing nonlinear hydrodynamics. However, nonlinear kinematics has received very little attention, as few models yet consider six degrees of freedom and large rotations. This paper implements a nonlinear hydrodynamic and kinematic model for an archetypal floating structure, commonplace in offshore applications: an axisymmetric spar-buoy. The influence of nonlinear dynamics and kinematics causing coupling between modes of motion are demonstrated. The nonlinear dynamics are shown to cause parametric resonance in the roll and pitch degrees of freedom, while the nonlinear kinematics are shown to potentially cause numerical instability in the yaw degree of freedom. A case study example is presented to highlight the nonlinear dynamic and kinematic effects, and the importance of including a nominal restoring term in the yaw DoF presented.</jats:p>

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

“…Hong et al [38] first introduced this case study, performing modelscale tests on the floating cylinder in a wave tank. Numerous authors then investigated various aspects relating to the dynamic instability and parametric excitation of the cylinder using numerical models [8,[39][40][41][42][43][44][45]. A schematic of the cylinder is shown in Fig.…”

A Real-Time Detection System for the Onset of Parametric Resonance in Wave Energy Converters

“…The selection of this type of WEC stems from the numerous reports of parametric pitch/roll for axisymmetric heaving point absorbers [17][18][19][20][29][30][31][32][33][34]39,41,45,46,[48][49][50]. The particular geometry used in this study is a representation of a classic spar platform from the literature [62][63][64][65], comprising a simple vertical cylinder whose natural period of pitch motion is about twice the heave resonant period. The 2:1 ratio of heave to pitch natural frequency makes the floating cylinder prone to parametric excitation in pitch.…”

“…Gavasoni et al [64] employed a numerical model for the investigation of nonlinear vibration modes and instability. Giorgi et al [65] demonstrated the potential yaw instability which may arise when including nonlinear kinematics in a nonlinear hydrodynamic model. This particular spar-buoy was chosen since it is well known to exhibit parametric resonance and there exists a validated numerical model able to capture the existence of parametric resonance (see Section 3.3).…”

“…This particular spar-buoy was chosen since it is well known to exhibit parametric resonance and there exists a validated numerical model able to capture the existence of parametric resonance (see Section 3.3). However the spar-buoy's geometry is much larger than would be used in wave energy applications, with a heave natural period T n,3 = 29 s and pitch natural period T n,5 = 57 s. Thus the geometrical properties will be normalised in the analysis to provide insights for performance on smaller scale geometries, such as WECs, following the normalisation utilised in [65], where the frequencies are normalised against the pitch natural frequency w n,5 and the wave heights are normalised against the metacentric height GM.…”

Dynamic Analysis of Suction Stabilized Floating Platforms

“…A comprehensive study of various nonlinear hydrodynamic models applicable towards designing an efficient wave energy converters is detailed in [18]. A nonlinear kinematic and hydrodynamic model was utilized for the dynamical analysis of roll, pitch and yaw instabilities and the occurrence of parametric resonance for an axisymmetric spar-buoy structure in [19]. The application of an active control system in a bottle shaped spar to control pitch disturbances is discussed in [20].…”