correlated and combined with each other, we can get the response of a single roll, sway, 
or yaw and so on, to the wave (either slope or height), as frequency response functions by 
solving the simultaneous equations of motion of the necessary degree of freedom, consid- 
ering the waves as only one source of excitation. 
This is not the case, however, when one output must be considered as the response 
to many related inputs. Shown here is an example that this author encountered in the 
analysis of a ship’s motion and stress. The ship was a cargo liner on the New York line, 
under service in winter on the North Pacific Ocean.*4 The relative wave heights of en- 
countering waves were measured by an on-board ultrasonic sensor located on the side of 
the hull near midship. Because of the poor position of the measuring device, no attempt 
was made to convert the readings to absolute encountering wave heights. However, the 
real encountering waves are only one input to the stresses and the motions of the ship. In 
analyzing the transverse stresses induced on the web frame near midship, this author tried 
to express the effect of real waves by the relative wave heights measured at the side of the 
ship and by supplementing with other inputs like rolling, pitching, and vertical accelera- 
tion measured at the same time. These additional inputs were correlated with each other, 
as shown in Fig. 3.12, and multiple input analysis techniques were adopted to analyze the 
response. 
OTHER MOTIONS 
x 
{ X9 Yo y 
PITCHING ————_—_——> ©) STRESS 
x 
{ 3 Y¥3 
OTHER " WAVE HEIGHT 
EFFECT: 
HEAVING 
Fig. 3.12. Multiple inputs interpretation. 
(From Yamanouchi.?3) 
With stress as the output and such inputs as relative wave height, rolling, pitching, 
and vertical acceleration, and with various numbers of inputs, the effects of some particu- 
lar inputs were investigated by checking the multiple and partial coherencies that show 
the effects of a particular input in the presence of one or more other inputs. 
Another trial investigation was the analysis of nonlinearity of output to input. Con- 
siderations on nonlinearity that provide another reason for getting a poor coherency 
function are generally treated in Part II of this lecture, but for convenience one trial is 
described here in relation to multiple input analysis. Figure 3.13 is an example of a record 
of simultaneous measurement of many responses of this ship such as roll, relative wave 
height, vertical accelerations at four points, stress on the web frame, revolution and 
torque of the propeller, helm angle, yaw, encounter time of waves to the stern, and so on. 
Some of the responses were picked up, sampled, digitized, and punched on a tape after 
the test. (At that time data were processed using punched tapes.) 
77 
