422 BELL SYSTEM TECHNICAL JOURNAL 



PART III 



AMPLIFICATION FACTOR 



3.1 Introduction 



If the maximum acceleration, of the packaged article as a whole, is 

 reached very slowly, the severity of the disturbance experienced by a 

 structural element of the packaged article is very nearly proportional to the 

 maximum acceleration. Roughly speaking, "very slowly" means that the 

 time, during which the acceleration undergoes a major change in magnitude, 

 is long in comparison with the natural period of vibration of the element 

 under consideration. When this is so, no transient vibration is excited in 

 the element. The displacement response of an element under very slowly 

 varying conditions is called the "static response". Under more rapidly 

 varying conditions the dynamic response to the same maximum acceleration 

 may be greater or less than the static response. The ratio (A) of the maxi- 

 mum dynamic response to the static response is called the amplification 

 factor. In general, for a given acceleration disturbance, very low-frequency 

 elements have amplification factors less than unity, while the amplification 

 factors are greater than unity for elements whose natural frequencies are 

 near or above the disturbing frequencies. The numerical value of the 

 amplification factor depends not only on the manner in which the disturbing 

 acceleration varies with time, but also on the "reference acceleration", i.e., 

 the value of acceleration for which the static response is calculated. Usually 

 the reference acceleration chosen for calculating the static response is the 

 maximum value (G„j) of the disturbing acceleration. However, when 

 special circumstances are being investigated, such as the effect of damping 

 or abrupt bottoming, the reference acceleration is taken to be Go , which is 

 the acceleration that would be reached if the damping or bottoming were 

 absent. In such cases the amplification factor includes both the effect of 

 rate of change of acceleration and the effect of the special conditions. 



When the reference acceleration is Gm the amplification factor will be 

 denoted by /!,„ and when the reference acceleration is Go the amplification 

 factor will be denoted hy A^ . The symbol Ge will be used to designate the 

 slowly applied acceleration that would produce the same maximum dis- 

 placement as the transient acceleration, i.e., Ge = AjGm or Ge = AqGo. 

 The symbol Gs will be used to denote the safe value of Ge , for an element 

 of the packaged article, as determined by a strength test or by calculation. 

 In specifying Gs some judgement is required to take into account the effects 

 of plastic deformation in comparing tests made on greatly different time 

 scales. Good judgement is also necessary in deciding whether or not the 



