13 27 



In the case of a complicated structure such as the side of a ship, 

 several different diffraction times and swing times may be distinguished, ac- 

 cording to the dimensions of the part of the structure that is under consid- 

 eration. Thus there will be a diffraction time and a swing time for the 

 motion of the segment of a plate between two adjacent stlffeners, and longer 

 times for the motion of the stiffened plate as restrained by bulkheads or 

 belt frames. 



The characteristic times are useful in classifying the various 

 cases that may arise. There are two simple cases which are particularly use- 

 ful to bear in mind as a background in considering more complicated situa- 

 tions. These two cases will be discussed in some detail. 



THE CASE OF LOCAL ACTION 



The typical situation contemplated in the preceding discussion was 

 distinguished by the condition that 



r„« T„ T„«T, [9a, b] 



where the symbol « means "is much less than," In other words, the compliance 

 time is several times shorter than either the diffraction time or the swing 

 time. The diaphragm acquires maximum velocity and cavitation sets in before 

 diffraction from the edge has had time to Influence the motion appreciably, 

 and also before the stresses in the diaphragm have produced appreciable ef- 

 fects. The action in such cases is essentially a local one, since, in large 

 measure, each element of the target is set in motion by the wave independent- 

 ly of other elements. 



This case can occur only provided the time constant of the wave, 

 r,, is not too long. It is sufficient, for example. If r„4C T^ and r„« T,, 

 that is, if the action of the wave is completed in a time much shorter than 

 either the diffraction time or the swing time. 



An especially important feature of the case of local action is that 

 in this case the conception of conveyance by waves is valid for both energy 

 and momentum. Any part of the target can receive at most only so much energy 

 as is brought up to that part by the incident wave; and part of this incident 

 energy will usually be reflected back into the water. The momentum brought 

 up to each part of the target, also, must be either taken up by the target or 

 reflected. Since momentum is a vector quantity, however, the laws of its re- 

 flection are more complicated than are those for the reflection of energy; 

 the momentum delivered to the target may be greater than that brought up by 

 the incident wave, up to a maximum of twice as much if the target is rigid. 



