transmission coefficient curve. In this region one must be careful of 

 the analysis because there are certain "irregular frequencies" or "John" 

 frequencies where the approach adopted here breaks down mathematically 

 (John, 1950) . These are described with reference to the integral equa- 

 tion technique by Frank (1967) . It is extremely difficult to predict 

 where the first of these irregular frequencies will occur when the 

 breakwater cross section is as complicated as the Friday Harbor break- 

 water. If this cross section were rectangular with the same exterior 

 dimensions as the Friday Harbor breakwater, then the first irregular 

 frequency would occur at B/L - 1.7, In practice, one may watch for this 

 mathematical phenomenon by checking the determinant of the matrix invert- 

 ed to solve the system of equations. In fact, this does decrease in the 

 region of B/L of 1.7 but does not indicate a singular matrix for the 

 calculation in this region of B/L. Since this is beyond the frequency 

 range of primary interest, it is best to simply view the results at B/L 

 greater than 1.7 with extreme caution. The oscillations in the trans- 

 mission coefficient in this region of B/L are probably the result of 

 these irregular frequencies. 



b. Breakwater Motions. In the wave channel experiments perform- 

 ed to date, there has been no attempt to compute the breakwater motions. 

 While the transmission coefficient is the primary measure of breakwater 

 performance, the motions may be very important to the designer, parti- 

 cularly if boats are to be tied to the breakwater. For the theoretical 

 analysis, this is a critical intermediate step where extensive experi- 

 mental measurements used for comparison would be invaluable. 



Friday Harbor Breakwater . The theoretically predicted 

 motions of the Friday Harbor breakwater are shown in Figures 14, 15, and 

 16. The motion response is almost the same as one would expect from an 

 uncoupled spring, mass, dashpot linear system. The only unusual 

 behavior is the null response in heave at B/L of about 0.75. This null 

 occurs at a point where there is a phase shift in the "added-mass" force ^ 

 a phenomenon which has been observed in experiments with catamaran- type 

 cross sections (Lee, Jones, and Bedel, 1971), and is a result of resonant 

 wave conditions within the open well of the catamaran. 



c. Mooring Line Forces. In recent years a great deal of effort 

 has been expended in understanding and predicting mooring line perfor- 

 mance, particularly for moored ships and drilling rigs (e.g., American 

 Society of Civil Engineers, 1971) . Wliile many of these analysis techni- 

 ques could be applied to the moorings of floating breakwaters, this has 

 not been done to date. There are also very few model-scale experiments 

 in which mooring forces have been measured and only a few cases where 

 good field data are available. 



Two techniques for calculating the spring constants for mooring 

 lines have been used. At first the catenary equations were applied to 

 find the change in force per unit displacement. While this approach 

 leads to a fairly simple algorithm for the calculation, there are a few 

 problems. In several cases spring constants were needed when the mooring 



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