Experimental Study on Parametrically Excited Oscillation of a Spar-Buoy Under Mathieu Instability

Abstract

The occurrence of the Mathieu-type instability was investigated theoretically and experimentally. The main aim of this paper is utilization of auto-parametrically excited oscillation to increase efficiency of wave energy converters. In this paper, the subject is the auto-parametrically excited oscillation of a spar-buoy type point absorber with the coupled motions of pitch and heave. A spar-buoy model with innovative ballast control system was made and the model experiments were carried out to realize the large oscillating motion based on the Mathieu-type instability. The ballast control system installed in the buoy model can make the ballast move in the vertical direction to realize a certain change of the pitch natural period. Free-decay experiments were performed to determine the natural frequencies and damping ratios with different ballast positions. During the experiments in regular waves, it was observed that the pitch motion became unstable and the large pitch occurred suddenly. Based on time histories of experimental results, the points (peaks and troughs) are extracted near the large pitch occurring and the periods of transient states were calculated to derive the parametrical values of stability. Considering these values with plotted stability chart of Mathieu equation, the occurrence of the large pitch motion is discussed.