310 



order not to limit unnecessarily the range of applicability of the theory. 

 The equations of the theory and the assumptions on which they are 



based are presented in the following paragraphs. 



(a) Equations and assumptions . — (l) Equations governing axially 



symmetric motion of a plate . The equations governing the axially symmetric 



motion of a plate, derived in Appendix A for the case of small thickness, are 



f- iT^lW <^. - Tf-r("Ti) ^ S^ , o. 



(2) 



where Cl- and CL> are the vertical and meridional accelerations, respectively, 

 given by 



^- • ^'^^ ^ Triz ^*^' (3) 



dr 





f 



where 



'V3W . 3, 



c>tc _ / 3t 





(5) 



~9r »'*' 



In these equations r and z are the radial and vertical coordinates, respec- 

 tively, of a point on the neutral surface of the plate (see figure 1), and wL 

 is the radial displacement of that point from its initial position to its 



