DYNAMICS OF PACKAGE CUSHIONING 



457 



Hence, the strain at the attached end of the bar is 



nirat 



El 



7ra n=l,3,5- 



2€ 



mra 

 2 



4v 



■aV 1 



sin 



ira ,1=1,3,5 ■ 



nirat' 



(4.3.25) 



(7nra \^ 

 2^0 



The two series may be summed, as before, with the result 



--= (-1) 



V 



+ (-1) 



COof . 



tan — sm coo 

 a 



2H 



a 



tan '^^^ sin coo I / 



tan — sm W2\t — ) 



La \ a / 



+ cos 



2k( 

 a 



- 1 



cosc^oU'- — )- 1 (4.3 



.26) 



Once more, the expression for the strain at the attached end of the bar is 

 in a form suitable for rapid calculation and it can be shown the e in equation 

 (4.3.26) for / ^ 7r/aj2 is never greater than the e in equation (4.3.14) for ^ 

 / ^ tt/coo for the samecoi/co2 . Hence, Fig. 4.3.2 and the conclusions follow- 

 ing equations (4.3.15) and (4.3.16) need not be modified. 



Notations 

 A Cross sectional area of a bar element of the packaged article. Also, a 



constant of integration. 



Ao 



A^, 



Amplification factor when the reference acceleration is Go. Ratio of 

 maximum dynamic response to the response to a slowly applied ac- 

 celeration of magnitude Gog. 



Amplification factor when the reference acceleration is Gm. Ratio of 

 maximum dynamic response to the response to a slowly applied accelera- 

 tion of magnitude Gmg- 



In Section 1.15, the sum of all the trapezoidal areas from .V2 = to Xi = 

 (xijn. M.SO, in Section 4.2, the coefficient of the nth term of a series. 



The area of a trapezoid with altitude ^{x-ijn and sides P„_i and P„. 



xa/l in the tension spring package. Also, in Part IV, the velocity of 

 propagation of longitudinal waves. 



