MS Thesis R. Hager - Hawaii National Marine Renewable Energy ...

Thus, Eq.(49) may be written as:FR ( MijUjBijUj) (52)i jwhere, B ij denotes the damping coefficient, which represents a reduction in harmonicoscillation via energy extraction. The variable M ij denotes the added-mass coefficient, whichdescribes the inertial and mass forces. Note B ij and M ij are symmetric tensors as given inAppendix A. M ij and B ij are functions of frequency of oscillation, the geometry, displacement,water depth, and distancing to surrounding bodies.Damping Coefficient for a two-dimensional single, heaving bodyRecall the boundary conditions are at the seabed, the body, and positive and negative infinityalong the x-axis. The derivation is given in Appendix A. The damping coefficient for a twodimensional,heaving body is:22gCg Bij(53)23.3.4 Haskind-Hanaoka RelationshipWhen the diffraction potential is unknown, the excitation force may still be calculated if theradiation and incident potentials are known using the Haskind-Hanaoka relationship(Newman, 1977). Recall the complex amplitude of the excitation force per unit waveamplitude is:X ( )n dS (54)iSD47Ii