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

Abstract

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.

A Computationally Efficient Analytical Modelling Approach for Parametric Oscillations in Floating Bodies

“…In this Section, the 1 DoF analytical model of a floating buoy in heave developed in [55] is first detailed, and then, extended to 2 DoFs by introducing the pitch model of motion.…”

“…( 10), with the radiation force and nonlinear restoring force terms, Eqs. ( 6) and ( 8), provides the analytical model for parametric resonance developed in [55]:…”

“…The geometry for the floating body used in the test case is an axisymmetric spar-buoy, similar to that examined in [55], composed of a truncated cone and a cylindrical extension, as shown in Fig. 2.…”

“…Recently, [55] developed an analytical model to capture the heave-to-heave parametric instability in order to investigate the possibility of designing a wave energy converter to leverage this phenomenon for increased power capture. For this case, the occurrence of parametric resonance in heave was not induced by the nonlinear hydrostatic stiffness term, rather [55] derived a wave excitation force term with time-varying coefficients, dependent on the oscillating heave position, that was able to capture the occurrence of parametric resonance. The analytical model in [55] demonstrated significant improvements in computational speed and comparable accuracy to a NLFK model for the test case of a heaving spar-buoy with a non-constant cross-sectional area.…”

“…This paper aims to investigate the feasibility of generalizing the computationally efficient analytical model in [55], by extending it from a 1 DoF system (heave only) to a 2 DoF system (heave and pitch). This extension will enable the study of heave-to-pitch Mathieu instability in addition to heave-to-heave Mathieu instability, providing a more comprehensive understanding of the dynamics of floating structures.…”