283 



THEORETICAL INVESTIGATION OF CAVITATION PHENOMENA 

 OCCURRING WHEN AN UNDERWATER EXPLOSION IS 

 INCIDENT ON A YIELDING SURFACE - III 



H. N. V. Temperley 



April 19 45 



Swnmary . 



In t*o previous reports, reTerred to as l(l) and I I (2) the problem of damage to a plate 

 with clamped edges and a baffle is considered on the alternative assumptions that water can or 

 cannot stand tension, the plate being subjected to a normally incident exponential pulse. In 

 the present report, some of this work is extended to oblique incidence, and, in addition, the 

 effect of the plate being supported by stiffencrs as well as at the edges, is being considered. 

 For cases in which the radius of the plate is small compared with the "wave-length" of the pulse, 

 it has already been shown in II that regions of tension in tne ivater do not occur to an/ extent, 

 so that the damage will be the same whether water can stand tension or not. It is therefore 

 only necessary to consider cases in which the radius is comparable with or large compared with 

 the "wave-length". The discussion shows that for radii large compared with the "wave-length" 

 cavitation should increase damage, and that for a structure like a ship's bottom or a panel of 

 plating divided up by stiffencrs this sho'ilo De true for practically all cases for which 

 cavitation is important at sU. For a structure like the box-model, on the other hand, there 

 seems to be an appreciable region of values of the variables in which cavitation reduces damage, 

 and this region seems to cover most of the cases occurring in practice. This last conclusion is 

 only valid if it is possible to neglect the effect of diffraction if extensive cavitation occurs. 

 Qualitative reasons for thinking this are civen. 



List of Symbols . 



''m ~ Maximum pressure of incident pulse. 



i// = Angle of incidence of pressure-puUe. (Acute angle between wave-front 

 and plate). 



- Time constant of incident pulse. 



C - Velocity of sound in water. 



p = Density of wat;-r. 



X = Distance from centre of plate along axis of plate. (Also thickness of 

 layer of water on plate). 



y = Deflection of plate. 



z = OistanCL measured parallel to plate and in plane of propagation of pressure 

 pu 1 se . 



R = Bad i us of plate. 



N = Number of sub-panels into which plate is divided by stiffoners. 



p = Density of plate. 



h = Thickness of plate. 



a ^^ Yield stress of plate. 



