Nonlinear Analysis of a Heaving Point Absorber in Frequency Domain via Statistical Linearization

Abstract

The majority of wave energy devices operate close to resonant conditions to enhance energy conversion resulting in large displacements. As a result, nonlinearities significantly contribute to the dynamics of the system. A typical approach to predict the behavior of the system and power output relies on the derivation of a mathematical model in the time domain to simulate the dynamics through some numerical codes. However, a relatively high computational demand is required for those simulations. In this regard, the present work deals with the nonlinearities in the frequency domain via Statistical Linearization. Two different power-take-off systems are investigated, a linear and a hydraulic one, and their mean power calculations are derived based on the Statistical Linearization. The reliability of the method is verified against the Power Spectrum Density (PSD) of nonlinear time domain simulations. Only the heave motion is analyzed, and several nonlinearities commonly reported for Point Absorbers (PA) were considered, such as cubic stiffness, geometric nonlinearities, drag forces, and Coulomb forces. The approach employed in this work offers a reliable estimation of body dynamics for all nonlinearities considered. In addition, the present method produced a fast estimation, which can be valuable for the assessment of several designs and sea load conditions.