TRANSIENTS IN MECHANICAL SYSTEMS 659 



First, we shall want to know the magnitude of the shock present in the 

 base or supporting structure; this will be called the "excitation." 



Second, the behavior of the resilient medium interposed between the 

 shock-producing base and the equipment. It is sometimes expressed as the 

 coupling. We shall use the term transmission. 



Third, the resulting disturbance of the equipment caused by the trans- 

 mitted shock, which we will call the response. 



The three functions do not exist independently, but are mathematically 

 related. For a clearer understanding of shock phenomena it is perhaps 

 helpful to fix in one's mind the idea that the response of a system is com- 

 pletely dependent upon the transmission function. 



To use an electrical analogue, the voltage ei (t) impressed upon a system 

 produces an output voltage 62 (/) which is completely defined by the trans- 

 mission function. For instance, if this transmission function represents a 

 filter of some kind with given boundaries, then it is to be expected that the 

 response of ^2 (t) is completely changed outside these limits and could even 

 be zero. The same train of thought will hold for mechanical systems. Here 

 the transmission function is mostly represented by the stiffness or the com- 

 pliance. For a completely rigid medium the stiffness would be infinite and 

 the input and output would be alike; in other words, a force applied to the 

 base would appear at the equipment. This is a theoretical case because no 

 material is perfectly rigid. Though some materials are more rigid than 

 others they will all give if the force applied is big enough. Now the forces 

 associated with a shock are almost always of considerable magnitude so that 

 the stiffness of a material becomes significant. 



As the stiffness diminishes the response changes and may appear to be 

 quite different from the input. As far as the transmissibility of forces is 

 concerned, the reader is reminded that a force is always accompanied by a 

 reaction. The forces which put the base into motion cannot be transmitted 

 by a soft material Uke rubber, unless it is compressed to extremely high 

 values, and thus produce an equally large reactive force. 



PART I 

 Analysis of The Excitation of the Base 



By recording the motions of the base, we obtain time-displacement curves 

 as shown in Fig. 2. The method of recording has been done by means of 

 high-speed motion pictures (at the Whippany testing laboratory using a 

 Fastex) and by using strain gages (at the Annapolis Engineering Experiment 

 Station). 



The test equipments are fundamentally mechanical impact producing 

 machines. For technical details and description of the machines the reader 



