71 



85 



Mi, = 2F, + - p{z\t - f) r,(s)ds 

 where D is the maximum diameter of the plate and 



[116] 



77(s) = — JdeJJ/(i', i/')/(i,2/)dx(ii/ 



[117] 



In which /(I'lyO is to be understood as expressed in terms of i, y, s, 6. If 

 s is too large, the Integral In i and y will vanish for certain values of 9; 

 and the entire integral vanishes for 

 s > D. 



Motion of the elements par- 

 allel to the initial plane of the 

 plate is ignored here, as usual. An 

 equation containing corrections for 

 motion of the baffle is obtained on 

 page 28 of the text as Equation [33]- 



The proportional shape may- 

 be supposed to be maintained by suit- 

 able internal constraint forces which 

 on the whole do no work in any dis- 

 placement of the plate. These forces 

 are in addition to those due to 

 stresses; they might be supplied, 

 for example, by a suitable llnkwork 

 mounted on the diaphragm. 



If ^'denotes the net force on unit area due to the constraints, the 

 element of work done by them is dW'= \(4>'dz) dS = 0, or, if z 

 as in [32], to allow for motion of the baffle, 



Figure 51 



^i + 2e/(x,v) 



dW = dzJ((>'dS + dz^j<t,'f(x,y)dS = 



But j^'dS is the total force due to the constraints and must vanish. Hence 

 j^'fix,y)dS = 0. The vanishing of this integral prevents 0' from contributing 

 to *. 



As a special case, if a circular diaphragm of radius a Is assumed 

 to remain symmetric about its axis but to become parabololdal in form, and 

 if z^ is taken to represent the displacement of the center, then 



f(x,y) =1 2 



[118] 



where r denotes distance from the center, and it is found that, whereas ri(a) - 

 for s ^ 2o, for 4 s < 2a 



