Testing Ship Models in Transient Waves 



The use of a signal with linearly varying frequency and constant amplitude 

 as an input signal removes these strong drawbacks to the pulse technique, how- 

 ever. Since it has constant amplitude, the input can be constrained to lie within 

 the linear range. With proper choice of sweep rate and starting frequency, the 

 controlled signals can have any desired energy level in each frequency band and 

 thus defeat to a great extent the effects of random measurement noise. 



Another strong advantage in the use of transients with a linear sweep rate 

 is that in many cases the entire transfer function of a system can be obtained by 

 cursory analysis of the transient records alone. If the rate of change of fre- 

 quency and amplitude is slow enough, the signals involved behave very much like 

 sinusoidal waves. From the integration method of stationary phase [2], it can 

 be shown that the amplitude of the transform at frequency co of such a signal is 

 equal to one-half of the single amplitude of the signal at the apparent local fre- 

 quency CO divided by the square root of the rate of frequency change (in cps/sec). 

 Such a computation was performed for the transient test shown in Fig. 13 for 

 the heave measurement. The results of this computation for the heave transfer 

 function are shown in Fig. 32. This figure compares the measurement and cal- 

 culation techniques and shows that there is good agreement among them. 



1.2 



1.0 



LEGEND 



A REGULAR WAVES 

 STATIONARY PHASE 

 O FOURIER TRANSFORM 



<0 





t^o 



.2 .4 .6 .8 1.0 



Frequency in cycles per second 



Fig. 32 - Comparison of methods of 

 analysis of heave response operators 



537 



