The linear equations for calculating the dynamic response of a two-body wave energy converter (WEC), which oscillates in the heave, or vertical, motion are derived. The two-body WEC comprises of a floating buoy, which is an oscillating pointabsorber, and a submerged intermediate buoy, which are connected via a power take-off (PTO) system. The intermediate buoy is anchored to the sea bed using a mooring system. In this analysis, the relative response between the floating buoy and the submerged intermediate buoy is determined. This relative response defines the motion which is transmitted to the PTO system and, thus, is the convertible motion used to generate energy. A case study using this methodology is also presented.
The derivation is based on the classical structural dynamics method of using the modal equations of a multi degree of freedom system. The natural frequencies and mode shapes of the system are determined and then used to transform the coupled equations of motion into the modal equations in order to individually solve a set of uncoupled equations for the system. These equations can then be solved using a single degree of freedom numerical solution. The hydrodynamic coefficients are calculated using commercial boundary element method software.
