Fixed-points-theory-based critical condition for [formula omitted] sprung mass isolation of a two-body point absorber in a sea wave environment

Abstract

The present research concerns a system that is composed of a heaving point absorber coupled with a sprung (overlying) mass. For this system we impose and address the requirement of sprung mass isolation from the buoy’s oscillation movement induced by the incident waves. To this end, the proposed passive control methodology builds on the related isolation approaches that concern the implementation of the H∞ optimization criterion in the Dynamic Vibration Absorbers (DVAs). Then, a novel H∞ optimization process is developed for the proposed wave-excited system to accommodate for the distinct challenges that arise due to the frequency dependence of the two-body system. To accomplish this, a “virtual” system is realized to temporarily bypass the frequency dependence of the actual system by capitalizing on the existence of the fixed points in the “virtual” system. The realized “virtual” system is embedded in an iterative framework to derive the pair of critical parameters (the tuning ratio δcrit and the damping ratio ζscrit) resulting in the formation of equal double peaks at the frequency dependent actual system. It is proved that any tuning ratio δ<δcrit combined with its corresponding damping ratio ensures the fulfillment of the H∞ optimization criterion. Moreover, any value of this pair is capable of controlling the global sprung mass acceleration maximum. Any conditions leading the “virtual” system to undesired solutions are investigated and eliminated from the optimization process of the actual system. The potential of the critical parameters to yield simultaneous broadband wave energy extraction is also demonstrated.