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

Due to Kirchhoff decomposition, recall:niinAdditionally, recall the total potential must satisfy the body boundary condition: nIDnon SApplying Eq. (13) to Eq. (54) the complex amplitude of the excitation force results in:Xi ni I D dS (55)SXiiD I idS (56)nnSSubstituting Eq. (11) into Eq. (56), the complex amplitude of the excitation force per unitwave amplitude is:Xi iI IidS(57) nnSComplex amplitude of the excitation force for a two-dimensional single, heaving bodyThe spatial part of the complex incident and radiation potentials in two-dimensions are: I gAi cosh( k(z d ))e cosh( kd )ikx gicosh( k(z d))Re cosh( kd )ikxAs given in Appendix A, by use of the Haskind-Hanaoka relationship, the complexamplitude of the excitation force for a two-dimensional body is:48