The Inerter Pendulum Vibration Absorber : with Applications in Ocean Wave Energy Conversion and Hydrodynamic Response Suppression

The annual power incident on the ocean-facing coastlines of North America is over 400 GW. Capturing a small fraction of this energy can significantly contribute to meeting energy demands. Therefore, there is a renewed research interest in converting energy from ocean waves. Typically, ocean wave energy capturing devices, known as wave energy converters (WECs), are placed in deep water as the wave energy is higher in the deep water compared to shallow water. To reduce the cost of installing and maintaining WECs in deep water, they can be integrated with existing offshore floating platforms in the ocean. For such integration, traditional WECs, operating on the principle of linear resonance, have a natural period in heave close to a typical wave period to generate a large heave resonant response and hence high-efficiency wave power production, which causes large platform motions. In other words, wave power production and hydrodynamic stability of the platform are conflicting objectives in traditional linear WECs. Therefore, simultaneous wave energy conversion and response suppression of the platform is necessary. To address this issue, in this work, a device known as an inerter pendulum vibration absorber (IPVA) is proposed combining the inerter with a parametrically excited centrifugal pendulum. Two system variations are studied: the IPVA and IPVA-PTO, marking the absence and presence of an electromagnetic power take-off (PTO) system. Both the IPVA and the IPVA-PTO are integrated with a single-degree-of-freedom (sdof) structure: a primary mass, and a spar, respectively. The efficacy in suppressing vibrations is studied in the case of the sdof IPVA system, whereas wave energy conversion and response suppression are analyzed for the spar IPVA-PTO. For both systems, a nonlinear energy transfer phenomenon in which the energy is transferred between the primary mass (or spar) and the pendulum vibration absorber. For the sdof IPVA system, it is shown that the energy transfer is associated with the 1:2 internal resonance of the pendulum induced by a period-doubling bifurcation. A perturbation analysis shows that a pitchfork bifurcation and a period-doubling bifurcation are necessary and sufficient conditions for this internal resonance to occur. Harmonic balance analysis, in conjunction with Floquet theory, along with the arc-length continuation scheme, is used to predict the boundary of internal resonance in the parameter space and verify the perturbation analysis. Furthermore, the effects of various system parameters on the boundary are examined. Next, the sdof IPVA is compared with a linear benchmark and an autoparametric vibration absorber and shows more efficacious vibration suppression. For the spar IPVA-PTO system, a similar analysis shows the nonlinear energy transfer, which is used to convert the vibrations of the spar into electricity while reducing its hydrodynamic response. Similar to the IPVA, a period-doubling bifurcation results in 1:2 internal resonance, which is necessary and sufficient for nonlinear energy transfer to occur. The hydrodynamic coefficients of the spar are computed using a commercial boundary element method code. The period-doubling bifurcation is studied using the harmonic balance method. A modified alternating frequency/time (AFT) approach is developed to compute the Jacobian matrix involving nonlinear inertial effects of the IPVA-PTO system. The response amplitude operator (RAO) in heave and the capture width of the spar IPVA-PTO are compared with its linear counterpart, and the spar IPVA-PTO system outperforms the linear energy harvester with a lower RAO and higher capture width. Experiments containing integration of the IPVA and the IPVA-PTO system with an sdof system (or "dry" spar in the case of IPVA-PTO) are performed in order to verify the analysis. Next, both the IPVA and the IPVA-PTO systems are integrated with a spar-floater combination and analyzed for their performance. Near the first resonance frequency, the spar-floater IPVA system shows a period-doubling bifurcation and energy transfer similar to the sdof IPVA system and outperforms the linear benchmark for hydrodynamic response suppression. On the other hand, the spar-floater integrated IPVA-PTO system is analyzed for its performance near both resonance frequencies. It is shown that near the first resonance, the spar-floater IPVA-PTO system's response undergoes a period-doubling bifurcation, and for small electrical damping, shows energy transfer. However, near the second resonance, secondary Hopf bifurcation is observed. A rich set of pendulum responses, such as primary and secondary harmonics, quasi-periodic, non-periodic, and rotation, are observed. Rotation provides the best energy conversion among all the identified responses. Finally, the electrical damping of the system is varied to find the optimal values for which the largest energy conversion occurs in the system, and it is found that the optimal electrical damping for energy transfer is associated with the pendulum's rotation.