SURFACE AND OTHER EFFECTS JfiS 



fications. Clearly, the pressures developed by an explosion both affect 

 and are affected by structures or targets in its neighborhood, and the 

 motions of the water and structure must be treated together as a single 

 dynamical problem. Even approximate treatments of simplified prac- 

 tical cases involve a large number of complications and variations, and 

 any attempt to present a reasonably complete picture of what is known, 

 and needs to be known, about such cases would require a volume at 

 least the size of the present one. Rather than ignore the subject en- 

 tirely, however, this and the next section are devoted to consideration 

 of greatly simplified and idealized situations. It is not to be presumed 

 that these correspond to actual problems, the intent being rather to 

 illustrate more simply some of the factors involved in more complicated 

 cases. 



A. Analysis of an infinite free plate. A simple example, which we 

 consider first, is that of an infinite free plate acted upon by the shock 

 wave from an explosion. ^ By free is meant that there is no constraint 

 to motion of the plate except that offered by its own inertia, and the 

 actual occurrence of transmissions and internal reflection of elastic waves 

 in the plate mil be neglected, the plate being assumed to move bodily 

 or not at all. (This effectively amounts to assuming an infinite velocity 

 of the elastic or plastic waves in the plate.) If this plate is initially 

 stationary, a plane pressure wave striking it will give the plate an initial 

 . velocity because of its finite mass for unit area of its surface. A reflected 

 wave of pressure will at the same time be transmitted back in the water, 

 w^hich must be of such magnitude that the resultant particle velocity 

 of the water in contact with the plate is equal to the velocity of the 

 plate. 



Let the plate have a mass m per unit area and velocity u, and assume 

 the incident pressure Pi to be a plane acoustic wave. If P2 is the pres- 

 sure in the reflected wave, Newton's second law for the motion of the 

 plate requires that 



(10.5) ^,^ = p^^p^ (^ = 0) 



at 



if distance x is measured from the plate into the water. The bound- 

 ary conditions at the plate are 



u = ui + U2 {x = 0) 



= (x = 0, ^ = 0) 



3 The motion of a free plate under various conditions has been considered by 

 several writers, notably G. I. Taylor (108), E. H. Kennard (57), and Emily Wilson 

 (see Reference (31)). 



