338 



2. Equation of Motion 



We consider a circular plate of radius R^ and thickness 3^ , 

 composed of material of yield stress V^ and density _p , The edge of the 

 plate is assumed to be clamped to a rigid supporting structure extending 

 a negligible distance beyond the edge of the plate. It is also assumed to 

 be backed by air on the upper sidey and to be in contact with water of 

 density j>^ on the lower side. The explosive wave advancing in the positive 

 B-direction is assumed to be of acoustical intensity and to be of exponen- 

 tial form p,« p«^e"^^. 



We will use the linearized equation of motion derived in Part I 

 for the vertical deflection i . For convenience, we repeat this equation 

 (Eq, (27) Fart I) here with the expansion parameter oc set equal to unity 

 and with the dropping of the superscripts referring to the first approxima- 

 tion: 



r* r 6>r\. ar / f 3o ' 



Here, we treat the water loading in the incompressive approxima- 

 tion, thereby neglecting retardation effects. In this case it is appropriate 

 to use Eq, (l/») of Part II: 



V (2) 



This result corresponds to a snail or nonexistait baffle; for an infinite 

 baffle, the teim p^ must be multiplied by 2, 





29 



