DYNAMICS OF PACKAGE CUSHIONING 



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that is, do is the displacement that would take place if the elasticity were 

 linear (see equation (1.3.1)) with a constant spring rate ^o equal to the initial 

 spring rate of the cubic elasticity. Also let 



B = 



Then, from (1.5.1), (1.5.2) and (1.5.3) 



(-1 + Vl + 5) 



B 



(1.5.3) 



(1.5.4) 



Equation (1.5.4) is plotted in Fig. 1.5.1 which shows graphically how the 

 maximum displacement dm compares with the "equivalent linear displace- 

 ment do" as the parameter B is varied. Note that B depends on the weight 

 of the packaged item, the height of drop and the shape of the load displace- 

 ment curve (as determined by .^o and r). 



Fig. 1.4.6 — Anomalous elasticity. Class F. 



Similarly we can compare the maximum acceleration G,„ with the maxi- 

 mum (Go) that would obtain if the load displacement curve were linear with 

 spring rate ^o • The latter acceleration is given by 



'^Jp (1.5.5) 



and the former is obtained by finding P^ from (1.2.17) and then, from 

 (1.2.16), 



Gm 



'Go 



V' 



/j/|(l + B)(-1 + Vl + 5). 

 Equation (1.5.6) is plotted in Fig. 1.5.2. 



(1.5.6) 



1 .6 Procedure for Fixdesg Maxevium Acceleration and Displacement 

 for cushionlng with cubic elasticity 



If the load-displacement curve of a cushioning system has the general 

 appearance of Fig. 1.4.2 (where the slope increases or decreases gradually 



