Applying Results of Seakeeping Research 



H(ajg) = system complex frequency response (system transfer function), 

 and 



$^^(ajg) = output function amplitude density spectrum 



into a so-called non-dimensional form, but in so doing forgets the precise notions 

 behind each quantity and assumptions and reasoning behind the derivation of 

 Eq. (1). 



Let us examine the problem more carefully by fixing attention on the inde- 

 pendent variable involved in Eq. (1). The frequency domain analysis of linear 

 systems in other engineering fields is precise in the sense that the analysis in- 

 volves a single, unambiguous "frequency." Unfortunately, in ship work this is 

 not the case, for we have two "frequencies" to play with; the absolute wave fre- 

 quency and the encounter frequency. This adverse fact causes much trouble and 

 the ensuing complications, especially in astern seas are, of course, due to the 

 fact that sea wave celerity is a function of wavelength. The question which 

 arises is which is our fundamental variable and why? Professor Lewis arbi- 

 trarily employs the logarithm of the absolute wave frequency and states that it 

 is "unnecessary to convert to frequency of encounter as originally proposed." 



The writer disagrees with this choice and suggests that the frequency of en- 

 counter is the basic variable because of the following reasons: 



(a) The frequency of encounter is the frequency which the ship feels and to 

 which it responds. 



(b) The ship-system is "non- stationary" and furthermore "directional." 

 Hence, ship speed and wave direction are not simply labels to families of graphs 

 but must be embedded in the encounter frequency. 



(c) The mathematical model of the ship system involves the frequency of 

 encounter and not the absolute wave frequency. 



(d) Equation (1) is strictly applicable only to system functions derived from 

 the mathematical model and relates them via the actual input density spectrum 

 to the actual response spectrum. 



There is, furthermore, a delicate point in the statistical process which 

 merits some attention. First of all there is an ambiguity as to what constitutes 

 the actual input function to the ship system. Is it the wave or is it the load 

 (force or moment) caused by the wave ? The answer depends on the definition of 

 the system. The physical system (the ship model), presents no difficulty and 

 what we measure in say a unit amplitude wave system is definitely related via 

 Eq. (1) to the wave. The mathematical system needs special care however; if 

 the Korvin-Kroukovsky tjrpe differential equations are used, then strictly speak- 

 ing, the calculated response must be related to the load, whereas if the Cummins- 

 type differential equations are used the calculated response must be related to 

 the wave. Whichever the case, however, the important point is that as regards 

 "inputs," wave amplitude or wave-induced load amplitudes have a definite physi- 

 cal meaning whereas "wave slopes" do not. Incidentally, the area under the 



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