JflS SURFACE AND OTHER EFFECTS 



values at points external to the plate. If the plate is circular with 

 radius a, the equalizing effect from the edge of the plate can occur only 

 after a time 6d = a/co after arrival of the incident wave at the edge. 



Kirkwood (62) has proposed as a criterion for the formation of cavi- 

 tation that the diffraction time must exceed the cavitation time at the 

 center of the plate. This cavitation time depends of course on the 

 motion of this part of the plate, but an approximation to the initial 

 motion is obtained by assuming the center to act as an element of an 

 infinite free plate of mass m per unit area (see section 10.5, part C). 

 If cavitation occurs when the resultant pressure on this element first 

 becomes zero, the time after arrival of an exponential pressure wave is 

 the Taylor cavitation time dc obtained in section 10.4, which is 



(10.21) e, = -^log,/3, where ^ = £?£f? 



jS — 1 m 



Kirkwood 's criterion may therefore be expressed for a circular plate by 

 the proposition that if dd exceeds dc cavitation will occur. Correspond- 

 ing estimates for other types of target and incident pressure wave can 

 be formulated in a similar way by suitable estimate of diffraction time 

 from the dimensions of the structure and its response to pressure. 



Although the simple criterion of comparing the diffraction and free 

 plate cavitation times is admittedly rough, its usefulness and approxi- 

 mate validity has been well established experimentally for small circu- 

 lar plates. A number of experiments have been performed, for example, 

 in which photographs were taken of the water in front of diaphragms 

 after arrival of a shock wave from a 50 gm. tetryl charge. Varying 

 cavitation and diffraction times were obtained by changing the radius 

 and thickness of the diaphragms. In all except borderline cases, cavi- 

 tation was found only when the time for arrival of a diffraction wave at 

 the center exceeded the cavitation time computed from Eq. (10.21). 



In the case illustrated in Plate Xllb, a steel diaphragm gauge plate 

 of 3.3 inch diameter, 0.084 inches thick, was struck by an exponential 

 wave of time constant 55 /jLsec. In this case the diffraction time 

 dd = a/ Co = 29^tsec. was somewhat greater than the cavitation time of 

 21 jusec, and the predicted cavitation near the center was observed, as 

 shown in Plate Xllb. 



It has also been found that positions of the cavitation ])oundary 

 calculated by similar methods are in good agreement with observed 

 values, and the simple cavitation criteria thus furnish a quite reliable 

 guide for analysis. The cavitation time is smaller for thin plates and 

 short durations of the incident wave, and the diffraction time increases 

 with the lateral dimensions. Cavitation therefore occurs for relatively 

 thin plates, or short durations of shock wave pressure. Many struc- 



