15 



THE EFFECT OF A PRESSURE WAVE ON A PLATE OR DIAPHRAGM 



ABSTRACT 



A systematic study of the phenomena attending the Impact of a pres- 

 sure wave upon a plate, usually a shock wave, is introduced by a discussion 

 of the commonest case, followed by the treatment of a number of special top- 

 ics: the various characteristic times that are involved; cavitation at the 

 interface; the transition to non-compressive action; the effect of a baffle; 

 formulas for the swing time and the deflection of a diaphragm; the factors 

 determining damage; and the departure from Hooke's law in water. 



The formulas are applied with fair success to some test data from 

 experiments conducted by the Bureau of Ships snd the David Taylor Model Basin. 



Most of the mathematical treatment is set down in an appendix to 

 the report. 



INTRODUCTION 



In ship design It would be a great advantage if effects of under- 

 water explosions on the structure could be calculated analytically. However, 

 the problem thus presented is one of considerable difficulty, especially for 

 contact explosions. Even in the case of the shock wave from a distant explo- 

 sion, and when the structure is idealized in simple form, complications arise 

 because the motion of the structure reacts back upon the water and thereby 

 modifies the pressure field. The treatment of this effect involves the solu- 

 tion of problems in the diffraction of waves. Further complications may 

 arise from the occurrence of cavitation. Only one case is easily treated 

 analytically; this Is the case of a plane plate or diaphragm of Infinite lat- 

 eral extent. 



The problem of a diaphragm loaded by a shock wave has been treated 

 several times by more or less approximate methods (1) (2) (3) (*+).* In his 

 second report on the subject, Kirkwood gave a general treatment in which ade- 

 quate allowance was made for diffraction (5) (6) (7) (8), and in a later re- 

 port the effect of cavitation was discussed (9)- 



It is the purpose of this report to collect the material that has 

 been assembled at the David Taylor Model Basin for attacking problems of this 

 kind and to consider its application to a few of the available data. The 

 material to be presented consists In part of analytical formulas and in part 

 of conceptions which are useful in thinking about the action of shock waves. 



Numbers in parentheses indicate references on page 62 of this report. 



