Effects of Heave Excitation on Rotations of a Pendulum for Wave Energy Extraction Bryan W. Horton, Marian Wiercigroch Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, Kings College, Aberdeen, Scotland, UK 1 Introduction The concept of mechanical pendula for wave energy extraction has been given a considerable attention in recent years. The parametric pendulum is a useful model of the heave excitation at the base of a suitably constrained floating pendulum, assuming linear Airy waves sufficiently describe sea states. Xu [1] has carried out a numerical-experimental study of this well known system with energy extraction. Xu & Wiercigroch [2] studied the existence of the rotational attractors through the parameter space and Horton et. al [3] proposed a ro- bust method for parameter identification of an experimental pendulum rig. Xu et. al [4] studied the effect the interaction between the excited pendulum and electrodynamic shaker had on pendulum dynamics. In addition, Xu & Wiercigroch [5] obtained closed form analytical expressions for the primary bifurcations leading to the existence of oscillations and rotations, respectively. All of the studies described above have focussed on pendula excited by har- monic forcing. While this is a valuable and necessary foundation to this study, a more rigorous representation of sea wave conditions is required. The purpose of this study is to provide a more representative wave ex- citation model by superimposing a stochastic component onto the standard harmonic parametric excitation. This study centres around observing and un- derstanding the effects such a forcing has on the stable rotational modes of the pendulum and we are interested in whether the phenomenon of stochastic resonance [6] is present. Blackburn et. al [7] proposed a model for a forced pendulum, adding an external forcing in the form of a stochastic noise. The authors studied how the added noise affected the lifetime of chaotic transients. In a later study Blackburn [8] provided a more indepth treatment of how an applied external stochastic forcing can cause the parametric pendulum to ex- hibit loss of stability of a periodic motion and stabilize once more. In this study the stochastic component of forcing shall be added in two ways: E. Kreuzer (ed.), IUTAM Symposium on Fluid-Structure Interaction in Ocean Engineering, c  Springer Science+Business Media B.V. 2008