Parametric resonance: a risk to be avoided or an opportunity to be exploited? A case for a 2:1 wave energy converter

Abstract

Accurate models for wave energy converters are paramount for appropriate and effective assessment of the system behaviour under operational conditions; if such models are also computationally efficient, they can be used for control and design applications. Crucially, the underlying design and working principle can be substantially modified only at early development stages and typically based on fast mathematical models with several iterations; since such models are often linear or weakly-nonlinear, complex nonlinear phenomena are rarely embedded into holistic design tools or optimization schemes. A secondary consequence is that nonlinearities are dealt with at a later verification and assessment stage and are typically a burden or an issue to limit. The aim of this paper is to highlight how nonlinearities can actually be a beneficial resource to be exploited and leveraged, rather than a bother. To do so, a computationally efficient nonlinear model is used, able to articulate relevant phenomena at a convenient computational time. The system under analysis is a prismatic floating wave energy converter and the nonlinear model implements an analytical formulation of Froude-Krylov forces computed on the instantaneous wetted surface; this modelling approach is able to articulate a 2:1 parametric resonance which, when activated under certain conditions, is a type of instability able to amplify the amplitude of motion. Note that the 2:1 proportionality refers to the ratio between wave and natural frequencies of the system. Therefore, this paper embeds parametric resonance into the notional design of a wave energy converter purposely designed to experience and take advantage of such an instability. Results are promising, since a substantial amplification is achieved in the 2:1 region, whereas similar or higher oscillation amplitude is obtained in the 1:1 region.