42 28 



Integrals extend only over the plate. The equation should also hold roughly 

 when there is no baffle at all provided 2F, is replaced by F, . 



If the baffle is movable, it Is more convenient to replace Equation 

 [28] by 



z =z, + z,(t)/(x,2/) [32] 



where z^ is the displacement of the baffle. Thus z,, refers, as before, to 

 the relative displacement between plate and baffle. If this expression for z 

 is introduced into Equation [l8], and if the equation is then multiplied 

 through by f{x,y) and Integrated over the plate, the result is 



d^ZA ., . .. dS' 



plate plate 



-£!n,.yHsf(^) ,fUW>'-f (331 



where 



B=ff{x,y)dS, M, = fmf{x,y)dS [3^a, b] 



Here B represents an equivalent area of the plate and Mj an equivalent mass, 

 both defined with respect to Interaction with the baffle. 



Comparison of Equations [33] and [29] shows that the relative mo- 

 tion of plate and baffle is affected by the motion of the baffle in the same 

 way as if, with the baffle fixed, the effective driving force 2F, + * were 

 replaced by 



Thus forward velocity of the baffle effectively decreases the load pressure. 

 If the motion of the baffle is accelerated, the relative acceleration of the 

 plate is further decreased in proportion to the acceleration of the baffle. 



The absolute motion of the plate Is then the sum of its relative 

 motion and the motion of the baffle, 



A more convenient form of the integral in Equations [29] and [33] 

 is given in Equation [^^6] of the Appendix. 



Unfortunately, the actual motions of plates or diaphragms under the 

 action of shock waves probably show little resemblance to any type of pro- 

 portional motion. This is brought out clearly by many observations which 

 have been made at the Taylor Model Basin; these will be described In other 

 reports. The study of proportional motion must find its justification in its 

 mathematical simplicity and in the hope that certain of its features as 



