660 BELL SYSTEM TECHNICAL JOURNAL 



is referred to the various test specifications by the Bureau of Ships (as^ for 

 example, Spec. 40T9). 



The characteristic of an impact is the transfer of mechanical energy from 

 one mass to another in a relatively short time. The corresponding force as 

 function of time is called an impulse, henceforth indicated as F{t). A study 

 of the pulse functions has suggested some probable theoretical shapes of F{t) 

 which could cover a wide variety of conditions. These pulse functions will 

 be used for force-time functions as well as displacement-time-functions and 

 it will be shown that the results are surprisingly similar. 



We will let these pulses operate on the base with mass mi and calculate and 

 plot the resulting time displacement curves. Since an impulse is associated 



2 

 ffl-1%1 



with energy transfer, it must be a function of — - . From the point of view 



1 1 1 1 1 1 1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 M 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 M M 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 M 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 



TIME >■ -»^ |<- 2 MILLISECONDS 



Fig. 2 — Time displacement record of medium high impact machine. 



of shock action, the final velocity v is extremely important, for it is this 

 velocity which will determine the displacement and acceleration of the 

 shock-mounted equipment. 



To distinguish the various applications of the pulse functions, the follow- 

 ing notations are adopted: 



/(/) represents any functions of /, without reference to its dimensional 

 magnitude. The transform of /(/) is indicated by F{s). 



x{t) represents a function of / when it is a displacement of the mars m 

 only. The transform is indicated by X{s). 



Xi{l) represents a function of / when it is a displacement of the base (with 

 mass mi) only. The transform is indicated by Xi(s). 



F(t) represents a function of / when it is a force applied to the base. The 

 transform is indicated by Fo{s). 



Since Xi{t) and F{l) are input functions, they may be represented by the 

 same type pulse, in which case the transforms are alike, i.e., F{s) = Xi(s) = 

 Fo(s). 



Figure 3A, a rectangular pulse, is the simplest form. 



Figure 3B is a triangular pulse, /(/), reaching a peak and returning to zero 

 in a linear manner. 



