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

Exploiting parametric resonance may enable increased performance for wave energy converters (WECs). By designing the geometry of a heaving WEC, it is possible to introduce a heave-to-heave Mathieu instability that can trigger parametric resonance. To evaluate the potential of such a WEC, a mathematical model is introduced in this paper for a heaving buoy with a non-constant waterplane area in monochromatic waves. The efficacy of the model in capturing parametric resonance is verified by a comparison against the results from a nonlinear Froude–Krylov force model, which numerically calculates the forces on the buoy based on the evolving wetted surface area. The introduced model is more than 1000 times faster than the nonlinear Froude–Krylov force model and also provides the significant benefit of enabling analytical investigation techniques to be utilised.

Numerical Analysis on Mathieu Instability of a Top-Tensioned Riser in a Dry-Tree Semisubmersible

The development of a dry-tree semisubmersible (DTS), a new type offshore hydrocarbon production system, is facing unconventional challenges in the issues of dynamic stability, structural integrity, and parametric resonance. The Mathieu equation is used to assess the dynamic stability of a top-tensioned riser (TTR) in order to prevent the parametric resonance which leads to detrimental effects on structural integrity. The objectives of this paper are to (i) study a Mathieu stability diagram and its coefficients for an assessment of the stability of a TTR, (ii) identify the effects of the dynamic tension variations in the Mathieu stability assessment, and (iii) analyze the stability of the TTR on a DTS, which is equipped with a long-stroke tensioner, by using numerical simulation. The dynamic tension variation in the DTS was identified to induce instability in the TTR. Hence, the Mathieu stability assessment is recommended to be included in an analysis of TTR behaviors in a dry-tree interface of semisubmersibles.

Experimental Study on Coupled Motions of a Spar-Buoy Under Mathieu Instability

A series of experiments were carried out to investigate the occurrence of the Mathieu-type instability. The main objective of this study is utilization of an auto-parametrically excited oscillation for wave energy converters. In this paper, the subject is the auto-parametrically excited oscillation of a spar-buoy type point absorber with two degrees of freedom. A small spar buoy model with a ballast controlling system was made and the model experiments were conducted to realize the large oscillating motion based on the Mathieu-type instability. The ballast controlling system is installed in the buoy model and the vertical movement of the ballast produces a certain change of the pitching natural period. Using the controlling system, the pitching motion in regular waves under the heave resonant period was measured. In some experiments, it was observed that the large pitching motion occurred suddenly, and the time histories showed different excitation pattern from the theoretical Mathieu-type instability. Based on the model experiments and considerations of the theory of Mathieu-type instability, the occurrence of the large pitching motion is discussed.

Experimental Study on Dynamic Control of Oscillation Characteristics of a Spar-Buoy

Experimental studies were carried out to investigate the possibility of utilization of auto-parametrically excited oscillation based on the Mathieu instability. For the simplicity, the subject is limited to the heaving motion of a spar-buoy type point absorber. The device consists of an inner cylinder and 12 outer cylinders. Each outer cylinder is equipped a movable floating column controlled by a ball screw mechanism and the buoyancy of the outer cylinders can be dynamically changed to induce the Mathieu instability. Based on results of the numerical simulation and the model tests, the possibility of utilization of auto-parametrically excited oscillation for WEC was shown.