298 - " - 



Piston Deflected Initially . 



In box model experirents, the target plate is already dished by the Shockwave before the 

 arrival of the bubble wave. It is necessary therefore to consider the case of the piston deflected 

 initially. 



Let y be the initial deflection. 



Then the equation of motion of the piston (s) becomes 



My + ky = f(t) - ky^j (It) 



where y is the additional deflection above y^^ and no deflection occurs until f(t) > ky^. 



The solutions of (it) for the finite baffle are: 



from equation (u) and taking fhu centre point value for the last term in (t) 



2 - expCnPp R 



_ = -J^ exp(-nt) + tH (2 sin qt - sin q(t - ^ ) 



"o - ^2,^2 q(n^*q2) 



2 - exp(-nR,) ) r 



-c- I exp(-nt ) {l + sin sin (qt + qt - 0)} for _i < t < CO (i5) 



,' 



where tan = - 



and ky = ( 2 - expi-'^) \ p exp 



^2 - exp(-"^,^ 



3(-nt.) 



from equat ion (5) 



My exp(-nt) 2n sin qt exp(-nt. 



n^q^ q(n^q2) ' q^ 



where ky = p exp(-nt^) 



{l ♦ sin 5 sin (qt + qt^ - 0)} 



for < t (16) 



Evaluation of y^ 



The initial deflection y is assumed due to the shock wave. In general, the distance of the 

 charge from the target and the distance of the bubble minimum arc not the sam;. 



Let d be the distance of the charge from the piston, 

 o 



d be the distance of the bubble minimum from the piston. 



p be the maximum bubble wave pressure at unit distance, the corresponding valve at 

 , 



any distance r being assumed to be P^'r. 



Then, assuming the total energy in the shock wave to be five times that in the bubble wave 

 at the same distance, the total shock wave energy per unit area 



5 P ^ 1 



= ■_ ^ - 



pc d^ n 



It is now assumed, as observed experimentally, that the static energy absorbed in producing 

 an initial deflection y is equal to the total shock wave energy incident on the target. For the piston 

 this condition is that 



