Iim(r )^ = {mrf 

 max 



co'- nTT 



+ K<-r-^^K-:;rp-_ 



2K 2 



,.(|.^K.j,-iy 



V2] 



(13) 



where j3 is the parameter defined previously, Equation 11, and K = nir/jLi. The solid 

 dot in Figure 14 is the stress calculated from Equation 13 at that particular value of 

 ^ and p. The values of I^^qxI °^ determined from Equation 13 were used in plotting 

 Figures 15 through 22 as and when necessary. The apparent discrepancies in the 

 computer calculations are considered to be due to roundlng-off errors inherent in 

 the computational procedures. 



Figure 23 is included to indicate the variation of jljnaxl ^'^^ ^ ^°'' ° Particular 

 value of M- Figure 24 shows the variation of maximum dynamic stress for the highest 

 frequency range 7t/5 ^ co' s 7.077 for particular values of jS and fi. As can be seen, 

 the maximum dynamic stress is highly dependent upon the nondimensional frequency. 

 Since in any application of these curves the peak values of I^^qxI "^^^^ '^® consid- 

 ered, the results for this range of frequencies are presented in a simplified form in 

 Figures 25 through 32, where each curve is drawn through the maximum values of 

 ll' I in the same manner as the dashed line in Figure 24. Each graph is drawn for 

 various values of fl a\ a given j3. In certain instances, it was again found necessary 

 to determine |^qx| °^ frequencies near it and its multiples by use of Equation 13. 



DISCUSSION OF RESULTS 



The results obtained from the computer program as outlined above are generally 

 in agreement with those quoted in the A. D. Little report' except for values of the 

 nonnalized maximum dynamic stress, l^^axl' corresponding to nondimensional 

 frequencies, co', near or equal to 3. 142. The computation of |^maxl °*' ^ ~ '"^ 

 according to Equation 13 gave results which compare favorably with those obtained 

 from the computer program. A comparison of three typical results is given in Table I. 



It should be noted that the value of I^qxI computed from Equation 13 is not 

 necessarily the peak value, since resonance will occur at nondimensional frequencies 

 other than 77 depending upon the values of ^ and y,. When fi approaches zero, the 

 resonant frequencies approach 77, 2 77, 3 77, etc, and the value of |^ax| °^ detennlned 

 from Equation 13 may then be interpreted as the maximum value. This can be seen to 

 be true by inspection of Figures 15 through 22. 



