Nonlinear dynamics of a heaving spar-floater system integrated with inerter pendulum vibration absorber power take-off for wave energy conversion

A power take-off based on the inerter pendulum vibration absorber (called IPVA-PTO) is integrated with a spar-floater system to study its hydrodynamic response suppression and wave energy conversion capabilities in regular waves. The hydrodynamics of the spar-floater system is computed using the boundary element method with linear wave theory. With the wave height and wave frequency as the bifurcation parameters, it is found that the system can undergo two bifurcations: period-doubling bifurcation around the first resonance frequency (spar mode) and secondary Hopf bifurcation around the second resonance frequency (floater mode). The period-doubling bifurcation results in an energy transfer between the spar-floater system and the IPVA-PTO for small electrical damping values. As a result, the IPVA-PTO system simultaneously reduces the maximum response amplitude operator (RAO) of the spar and increases the normalized capture width in comparison with the optimal linear benchmark. Experiments performed on a "dry" single-degree-of-freedom system integrated with the IPVA-PTO where the base excitation is substituted for the wave excitation verify the simultaneous performance enhancement due to the period-doubling bifurcation. The system performance beyond the period-doubling bifurcation is also experimentally investigated. On the other hand, as the wave height approaches and passes the secondary Hopf bifurcation, the pendulum responses transition from primary harmonic responses to quasi-periodic responses to rotations. When the rotations occur, the IPVA-PTO system increases the maximum normalized capture width threefold to fivefold compared with the optimal linear benchmark, yet slightly increases the RAO around the second resonance frequency. Nevertheless, the RAO remains smaller than the global maximum RAO of the optimal linear benchmark. Finally, parametric studies are performed to study the effects of parameters on the bifurcations. It is observed that by varying the electrical damping, the wave height required for achieving the period-doubling bifurcation can be changed significantly, which can be exploited to stabilize the spar.