23 



^ 



/, 



/ 



Chprge 



Water 



/ 



Air 





Figure 7 - Schematic Illustration 



of the Deflection of a Plate 



without Cavitation 



No Cavitation: The Tension Phase 



If the water remains In contact 

 with the plate, as In Figure 7. tension 

 develops In It, and this tension tends to 

 arrest the motion of the plate. 



In the one-dlmenslonal case, 

 the plate Is thus brought to rest In the 

 end, and Its total displacement Is just 

 twice the displacement produced In free 

 water by the passage of the Incident wave; 

 see TMB Report 480 (10), page 25. This 

 case is Illustrated In Figure 5- If the 

 plate Is limited In extent, however, 

 forming part of a larger structure of 

 some sort, the Influence of diffraction 



will usually be such that the plate retains part of the velocity that It ac- 

 quired during the primary shock phase. If the shock wave Is of very brief 

 duration, the plate may come almost to rest and then be accelerated again as 

 the diffracted pressure Is propagated in from the edge. 



The analysis Indicates that the residual velocity left in the plate 

 should be of the order of the velocity that would be calculated by non- 

 compresslve theory with allowance for loading of the plate by the water; this 

 is verified in a special case in the Appendix. If there is open water beyond 

 the edge of the plate, the calculation should be made for a pressure equal to 

 the Incident pressure; in this case, although the pressure is doubled at 

 first by reflection, the doubling quickly fades away as diffracted waves ar- 

 rive from beyond the edge of the plate. If the plate is mounted in a large 

 rigid baffle, however, the doubling persists and the non-compresslve calcula- 

 tion should be made with twice the Incident pressure. 



The plate will then continue moving until it is arrested by forces 

 due to other parts of the structure. During the process of arrest, the ki- 

 netic energy in the plate and in the adjacent water becomes converted into 

 other forms, perhaps partly or wholly into plastic work. The time required 

 for the final arrest of the plate constitutes a fourth characteristic time, 

 which may be called the iwing time of the plate, denoted by T,. Here the 

 swing time under water-loading is involved. In the case of ships or compara- 

 ble models the swing time Is usually many times longer than the duration of 

 the A-phase of the pressure wave. 



Some formulas that may be used in making rough estimates of swing 

 times will be found as Formulas [65] to [68] on pages U3 and 44. 



