DAMAGE TO SHfP'S PLATES BY UNDERWATER EXPLOSIONS 

 S. Butterworth 

 July 1924 



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Summa ry , 



This paper deals with the effect of an explosive wave upon a circular plate in an otherwise 

 rigid wall separating water from air. It is assumed as a first approximation that the period of 

 free vibration of the plate is large compared either with the duration of the wave or the time 

 required for the wave to travel a distance equal to the diametfer of the plate. In these circumstances 

 the effect of the wave is to impart kinetic energy to the material of the plate and to the surrounding 

 water. It is considered that this energy by being partially converted to strain energy is the factor 

 producing distortion and (if largt enough) rupture of the plate. A formula for calculating this 

 energy (equation 29) is given. The formula indicates that the energy is proportional to the power 

 I*/? of the weight of the charge and to the inverse square of the distance from the charge. These 

 results are in agreement with those obtained in sea-trials. An attempt is made to estimate the 

 effect of the period of the plate in relation to the duration of the wave. The result expected is 

 that th.' W ^ law becomes w" where x is somewhat less than U/3 but must be greater than 2/3. A 

 comparison with the results obtained with copper-diaphragm gauges shows that the available energy so 

 estimated is about double that absorbed by the gauges. 



Ifature of explosive wav e. 



The experiments carried out by means of the piezcf-electric gauge show that the pressure wave 

 transmitted through water due to the detonation of a high explosive charge consists of a very rapid 

 increase of pressure followed by a much slower rate of dtcay and may roughly be imitated by an equation 

 of the type 



P = Po --™' (1) 



in which p is the instantaneous pressure, P the maximum pressure, t the time and m a constant for a 

 charge of given weight and nature. For a point at distance from e charge of given explosive having 

 weight * the records indicate that 



P = KW^'^/D, m = a/w^''^ (2) 



For T.N.T. if we put 



14,000, a = 7,400 (3) 



the pressure being measured in lbs. per square inch. W in lbs. and D in feet; equation (l) will 

 fit the recoras as regards momenta (/^ pdt) and energy (J~ p dt) but will give maximum pressures 

 about 20J highijr than the observed values. Since in the following notes wi; are concerned mainly 

 with momenta, the above constants will be tanen and if I is the momentum in lb. seconds crossing 

 one square inch 



^ P K v,^''? w2/3 



I = odt = -£ = - - = 1.9 - (4) 



J„ m a D D 



According to equation (l) this momentum requires an infinite time to be delivered but 

 actually the major portion is Jelivered in a very short time;. Thus 99S of the momentum will pass 

 in a time 



T = 4.6 W^''^/a 



so that if w = 1000 lbs., a = 7400, r = 0.006 second. 



For 



