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DIFFRACTION EFFECTS IN BUBBLE DAMAGE TO BOX 

 MODEL PLATES ENERGY CONSIDERATIONS 



G. Charlesworth 

 September 1945 



S ummary , 



Bubble damage in box model experiments has indicated that energy is diffracted from the rigid 

 flange on to the target plate. In this note, the effect of diffraction in a simplified system under 

 conditions similar to those in box model tests is calculated approximately. 



The system considered is that of a circular spring loaded piston moving in a finite fixed 

 rigid circular baffle under the action of a plane bubble wave. The velocity of the water outside the 

 baffle has been assumed equal to the particle velocity in the incident wave. An approximate solution 

 of the equation of motion including the effect of compressibility is obtained and, in a representative 

 numerical example, the deflection of the piston calculated from this solution is compared with the 

 deflections for an infinite plate and for both finite and infinite baffles on non-compress Ive theory. 

 The piston is assumed initially undeflected. It is found that the ratio of the maximum energy 

 absorbed by the piston to that incident on it for the finite piston is of the same order of magnitude 

 as that observed in box model experiments, which fs not the case for the infinite plate or infinite 

 baffle. It is also found that the maximum deflect ions for the finite baffle are about the same with 

 the compressive and non-compress ive approximation, though the deflection time-curves show that the 

 deflection is gr^'ater at earlier times in the former case. 



The calculations are then extended to the case of the piston deflected initially in a finite 

 baffle for both the compressive and non-compress ive cases. The ratio of maximum energy absoroed to 

 incident energy is evaluated numerically for conditions similar to those in R.R.L. box model experiments. 

 It is found that the energy ratio for the compressive approximation is in fair agreement with observation 

 and is better than the non-compress ive case. 



It is concluded from the calculations that the observed extra energy absorbed by the plate 

 above that directly incident on it in the bubble wave can be largely ascribed to diffraction effects 

 from the flange. 



Introduction . 



In a recent series of box model experiments it was found that the energy absorbed Oy the target 

 plate under the action of the bubole wave was more than twice that directly incident on it. It seems 

 likely that most of this onergy absorbed by the plate Is due to diffraction from the rigid flange round 

 the target plate. The present note is an attempt to determine approximitely the effects of diffraction 

 in a simplified syste^i consisting of a piston moving in a baffle and is essentially an extension to 

 bubble waves of Butterworth's analysis for shock waves (l). 



Assumptions . 



The system considered is a circular rigid spring loaded piston moving in a plane fixed rigid 

 circular baffle of finite rxtent. The distribution of norral velocity over the plane of the piston 

 and baffle is assuiieO to bo v over the piston, 2i ro over the baffle and equal to the particle velocity 

 in the incident wave outsid- the baffle. The assumed velocity outside the baffle is thus too siteII 

 at points near the baffle and will lead to an overestimate of the energy absorbed by the piston. The 

 incident wave is assumed to be plane. It is also assumed that the piston spring is 'plastic'. 



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