26 



12 



the diaphragm will be Influenced continually by the presence of water In con- 

 tact with it. Analytical treatment is easy in the one-dimensional case, pro- 

 vided the artificial assumption is made that cavitation occurs at a fixed and 

 known breaking-pressure; but the three-dimensional case presents considerable 

 difficulty. For this reason, only cavitation at the face of the plate will 

 be dealt with in the present report. The final deflection of the plate may 

 not be greatly influenced by the exact mode in which cavitation occurs. 



PART 2. THE VARIOUS TYPES OF ACTION BY A SHOCK WAVE 

 THE POUR CHARACTERISTIC TIMES 



In the foregoing discussion of a typical sequence of events, the 

 relative magnitudes of four characteristic times have played a determining 

 role. These times may be listed together as follows: 



1 . The time constant or approximate time of duration of the shock wave, 

 T^; this is equal to l/a, for an exponential wave characterized by the expres- 

 sion p = p^e'" ■ 



2. The compliance time T^ of the structure, or the time required for 

 the shock wave to set the structure in motion at maximum velocity; 



3. The diffraction time T^, or the time required for a wave to travel 

 from the center of the structure to its edge; 



4. The swing time T, of the structure, or the time required for it to 

 undergo maximum deflection and come to rest. 



An attempt to picture the significance of these four times in a typical case 

 is made in Figure ^^ . 



cTd 



I J 



Time 



- Diaphrogm 



Time 



Figure n - Illustration of the Significance 

 of Time Factors for a Diaphragm 



T^ is the time constant of a shock wave, 

 T^ is the diffraction time, 

 r„ is the compliance time, 

 Tj is the swing time, and 

 c is the speed of sound in water. 



