328 



magnitude, it has been proposed that cavitation vd.ll occur when the pres- 

 sure in the wave becomes negative. This is assumed by G. I. Tayloi^ in 

 his theory of plastic damage. The hydrodynamic theory developed in the 

 last section as applied to thin circular plates in Parts III, IV, and V 

 fails when cavitation is well-developed. Consequently, it is imperative 

 that the results of this part be amended by a reliable cavitation criterion. 



During the initial stages of its motion, the central part of the 

 circularly clamped plate will behave as a free plate ,since it will take a 

 finite time Ro/^* ^°^ ^ pressure wave in the water starting from the 

 periphery of the plate to perturb the pressure distribution near the cen- 

 ter. Furthermore, it will take a considerably longer time Ro/c for a 

 plastic wave in the plate to travel from the periphery to the center (se*. . 

 Part IV, Se«./|}lt has been shown by Kennard^ that for a pressure wave of 

 the form p^O^): p^ e." '* impinging upon a free plate of thickness a© 

 and density f , the pressure will drop to zero in a time 



d-e, "^ ©. M (16) 



o, - i'a./f^Co . J 



If this time is reached before the arrival of the pressgre wave from the 

 periphery a negative pressure will certainly be developed and we assinne 

 that caviation will occur. Thus we propose the following criterion: 

 f^«/c, > ®«, — cavitation 

 l?oAo < ^t - °o cavitation 

 If this criterion is in error, it probably underestimates the critical value 

 of Ro/c^ above which cavitation occurs, 



^ Private communication. 



2/ E. H. Kennard, David Taylor Model Basin Report, No. 480 (1941). 



19 



