Utilization of Nonlinear Resonance of Vessels for Ocean Wave Power Generation

Abstract

This paper presents a method to utilize the pitch-roll nonlinear energy transfer phenomenon in vessels for off-shore wave power generation. This paper builds on an existing design where the power generator is a horizontal pendulum on board a vessel. The surface waves result in rocking of the ship, which in turn results in rotation of the pendulum. The pendulum is connected to a DC generator to produce power. The coupled electro-mechanical system is modeled using energy methods. The design in this paper utilizes the nonlinear coupling between the roll and pitch motions of the generator vessel. The natural frequency of the roll motion of the vessel is tuned to be twice the fundamental frequency of the pitch motion. In this specific condition when the vessel is excited in the pitch direction, the energy is nonlinearly transferred to the roll mode and the vessel oscillates in the roll direction. It is shown that the combination of the pitch as well as roll motion is far superior to the pitch motion since the combination results in full rotations of pendulum. A pendulum in full rotations generates orders of magnitude more power compared to a locally oscillating pendulum.

Enhancing power generation of floating wave power generators by utilization of nonlinear roll-pitch coupling

“…As the waves excite the ship, the pendulum rotates and generates electricity. If the ratio of the pitch natural frequency of the ship to the roll natural frequency is 2:1, when the ship is excited in the pitch mode, the energy is transferred to the roll mode of the ship and that makes the pendulum rotate faster and thereby generate more power [25]. Figure 2 shows how the input ocean wave power is converted to the electricity using our device.…”

“…c is the damping coefficient of the pendulum and R is the resistor of the generator. Now in order to relate the non-inertial coordinate system to the inertial coordinate system, we use pitch and roll rotation matrices [25]:…”

“…Equations ( 6) and (7) include the backward dynamic interaction (BDI) effect of the pendulum on the vessel. If the mass of the pendulum is negligible to the mass of the vessel we can simplify the governing equations as [31]: ´-…”