The inertial force (or added^mass force) arises when the breakwater acce- 

 lerates, which also accelerates the fluid around it. The motion-gene- 

 rated waves are moving away from the breakwater and result in the wave- 

 damping term. A term representing the forces due to viscosity is in- 

 cluded, but these forces are neglected in the analysis. Experience in 

 ship motion analysis (Salvesen, 1970) has shown this to be acceptable 

 for all motions but roll, where damping may make a more significant con- 

 tribution than for sway and heave motions. At present, the main reason 

 for neglecting the frictional forces is that they lead to nonlinear 

 terms in the equations of motion, which make their solution far more 

 complex. Hydrostatic forces arise because of changes in the displaced 

 volume of the breakwater when it moves. In this analysis the mooring 

 forces are modeled as simple springs with their contribution to the 

 damping and inertial forces considered small in comparison to similar 

 terms resulting from the breakwater motion. The wave exciting force 

 results from the incident waves striking the breakwater. 



If we neglect the nonlinear terms and assume that the fluid is in- 

 viscid, then the equations of motion describing the coupled sway, heave, 

 and roll motions of the breakwater are of the form: 



3 



E {(m. . + M. .) a. + X. . a. + (KH, , + KM. .) a. } = F. (t) (2) 



for j = 1,2,3. 



The symbols are defined as follows: 



p. . = added-mass coefficient with the Wij <^^ representing the 

 added-mass force or moment in the jth direction due to 

 acceleration in the ith direction. 



X. . = damping- force coefficient relating damping force or moment 

 in the jth direction to velocity in the ith direction. 



KH.. = hydrostatic spring constant relating the restoring force or 

 moment in the jth direction to displacement in the ith 

 direction. 



KM. . = similar to KHj^^ but due to the mooring system. 



F. = exciting force or moment in the jth direction. 



In order to solve these equations, the physical mass and moment of iner- 

 tia, added mass and damping coefficients, static spring constants, and 

 the exciting forces must all be known. Mass and moment of inertia are 

 computed directly from the specifications of the breakwater section. The 

 KHij are derived directly from hydrostatic considerations in Appendix A, 

 while approximate values for KMj^j are obtained by using a discretized 

 approximation for the mooring line as described in Appendix B. Potential 



i6 



