428 BELL SYSTEM TECHNICAL JOURNAL 



It is required to judge the suitability of a proposed package for a large 

 vacuum tube weighing 10 pounds. Strength tests have been made on the 

 tube in a shock testing machine which produces a half-sine-wave acceleration 

 pulse of 25 milliseconds duration. The weakest element of the tube is 

 found to be the cathode structure, for which the safe maximum acceleration 

 in the drop testing machine is 200g. The cathode structure has a natural 

 vibration frequency of 120 cycles per second and has 1% of critical damping. 

 The proposed package has essentially linear, undamped cushioning with a 

 spring rate of 3300 pounds per inch and an available displacement of | inch. 

 The outer container weighs much less than the tube so that the package may 

 be expected to rebound. Is the cushioning suitable for protecting the 

 cathode in a drop of 5 feet? 



First find the maximum G that the tube will experience in a 5 ft. drop of 

 the package (equation 1.3.3): 



„ _ , /2hki _ , /2 X 60 X 3300 _ .^^ 



^-- Vw,~ V To ^^^- 



The accompanying maximum displacement is, from equation (1.3.4), 

 , 2h 2 X 60 „ , . 



^- = g; = -199- ='•'"• 



The available displacement (| inches) is therefore sufl&cient and the maxi- 

 mum acceleration {199 g) is slightly less than the safe maximum acceleration 

 (200g) found with the shock testing machine. However, before the cush- 

 ioning is approved it is necessary to investigate the frequency effects. The 

 duration of acceleration in both the shock machine and in the package 

 must be considered. 



The amplification factor for the element tested in the shock machine is 

 found as follows. First find the frequency corresponding to the 25 milli- 

 second pulse: 



U = i-— = 20 c.p.s. 



■' 2 X .025 ^ 



The ratio of the element frequency to the shock machine frequency is 



/i = ^ = 1^ = 6 

 fi 0)2 20 



Entering Fig. 3.2.2 witha)i/co2 = 6, we read, from the curve /3i = 0.01, Am = 

 1.14. The 200g test in the shock machine is, therefore, equivalent to a 

 slowly applied acceleration oiGs = 200 X 1.14 = 228g. 



