36 



22 



dt 



T = 2pi + 



>n Klt^l, 



dS 

 s 



[16] 



It Is readily shown that. If the plate remains accurately plane, 

 this equation reduces to the familiar one-dimensional equation; see the 

 Appendix. The relief term, or the term containing the integral in Equation 

 [l6], becomes the last or damping term in Equation [1]. Of, if plane waves 

 are incident at an angle d, and if = 0, so that the elements of the plate 

 move independently, Equation [l6] becomes, as shown by Taylor (U), 



m 



d'z 

 dt^ 



pc 



dz 



cos 6 dt 



= 2p, 



[17] 



The general equation is thus seen to be consistent with others that can be 



obtained more simply. The case of spher- 

 ical waves has been considered by Fox 

 (15). 



PLATE OR DIAPHRAGM OF FINITE EXTENT 

 SURROUNDED BY A PLANE BAFFLE 



In tests, a plate or diaphragm 

 is commonly mounted in a support that ap- 

 proximates a rigid baffle; such a mount- 

 ing constitutes a first approximation to 

 the mounting of a plate in the side of a 

 ship. In some cases it may be necessary 

 to allow for motion of the support. 



If only part of the structure 

 Just considered consists of a movable 

 plate or diaphragm, while the remainder 

 forms a fixed plane baffle, the Integral 

 in Equations [15] or [t6] need be ex- 

 Or, more generally, as is illustrated in 

 Figure 15, if the baffle is itself movable as a whole but remains plane, the 

 equation for the motion of any point of the plate can be put into the form, 



Figure 15 - Diagram Illustrating 

 Incidence of a Wave on a Plate 

 Mounted in a Movable Baffle 



The displacement of the baffle, assumed 



plane, is «i; the displacement of any 



point of the plate is z. 



tended only over the movable part, 



m 



d'z 



= 2p. •\- ^ - pc 



dz, 

 dt 



P. (LI. 



plate 



dh 

 'dtJ 



d'-z 



I, 



dS 



■i8] 



where z, is the displacement of the baffle, all quantities are taken at time 

 t except the values of the Integrand, and the integral extends only over the 

 plate; see the Appendix, Equation [109]. 



Comparison of the last equation with Equation [l6] shows that the 

 principal effect of motion of the baffle is to relieve the load pressure on 



