DYNAMICS OF PACKAGE CUSHIONING 



423 



assumptions listed in Section 0.2 are valid in each application. The general 

 procedure for using amplification factors is as follows. We first find the 

 value of the reference acceleration (in units of number of times gravity) from 

 Part I. From Part II we find the properties of the acceleration-time rela- 

 tion which give us the information required for entering one of the curves 

 of Part III and finding the amplification factor. Then, the product of the 

 reference acceleration and the amplification factor (/1,„G„, or AoGo) is a 

 number (Ge) by which the weight of the structure is to be multiplied when 

 calculating its deflection or stress by the usual static methods of elementary 

 strength of materials. Alternatively, G, must be found not to exceed Gs . 



i^d: 



(a) 



(b) 



Fig. 3.2.1 — Idealized system used in calculating amplification factors for linear undamped 

 cushioning with perfect rebound, (a) initial position, (b) first contact with floor. 



In the following sections the amplification factors for typical transient 

 accelerations encountered in package drop tests are calculated. The ampli- 

 fication factor curves that are plotted are entirely analogous to the familiar 

 "resonance curves" for steady sinusoidal vibration, except that in this 

 case the disturbing forces are transients of various shapes. It will be seen 

 from the curves that the maximum acceleration, as calculated by the 

 methods of Part I or as measured by an accelerometer, is not always a true 

 measure of the severity of the disturbance. 



3.2 Amplification Factors for a Half-Sine-Wavx Pulse 

 acceleration 



The first case to be treated is the response of an element of the packaged 

 item to the transient acceleration that would occur in a package with linear 



