DYNAMICS OF PACKAGE CLSIIIOXING 441 



with Class A cushioning the difference in maximum acceleration, rather than 

 the difference in amplification factors, is usually more imix)rtant. 



Example: Consider the example given in Section 1.6 and let it be required 

 to determine the effect of pulse duration on a cathode structure with a 200 

 c.p.s. natural frequency of vibration. In Section 1.6 we found that 



B = 5.4 ko = 255 



Go = 28.6 r = 108. 



Gm = 5^ 



With B = 5.4, enter Fig. 2.8.2 and find 



coo 



= 0. 



W2 



Now 



.. = y/|l = ^'-^^^^ = 66.1 rad./sec. 



22.5 

 Hence 



W2 = ^^ = 75 rad./sec. 



Then, with coi/co. = 27r X 200/75 = 16.7, enter Fig. 3.6.2 and find Am = 

 approximately 1 .0. Hence Ge is about the same as Gm and the conclusions 

 reached for this problem in Section 1.6 are not altered. 



3.7 Amplification Factors for Abrupt Bottoming 



The amplification factors for bilinear elasticity have not been computed 

 in complete detail. They can be obtained approximately by using the dura- 

 tion curves (Fig. 2.10.2) and the amplification curves for the linear case 

 (Figs. 3.2.2 and 3.5.2 to 3.5.7). It is useful, however, to calculate the am- 

 plification factors for extremely abrupt bottoming {kb —^ =o) to obtain a 

 general understanding of the accompanying phenomena. 



The system to be considered is illustrated in Fig. 3.7.1. It is assumed 

 that the impact between wz2 and the base (occurring at / = /s , ^'2 = ds) 

 has a coefficient of restitution of unity. Hence mo will strike the base with 

 velocity 



tel,=, = /2,*(l-|) 



(see equation (2.10.8)) and leave it at a velocity of the same magnitude but 

 opposite sign. Perfect rebound of the whole package is also assumed. 



