1159 
= 5 = 
ree goc S, (S, + n) 
=] RR Ea Soar ae 
mits, ine = e+ 2) 
(11) 
2 8, (s, + nl) 
m(S, — S,) (io ne + pe) 
and substituting these in (4), (5) and (8) 
B= sy qe Qe eat MeFi) e°2' + (n? +p”) ent 
Po ne WE + y m (S, - S,) m (S, - S,) 
(12) 
and 
2p rite Ty BISl thn got Set 
= —>. EE, e +—~— eo 1 - e2 
3 m(n® — EE + w*) SS, Stowe ee 
Oblique incidence. 
When the incident pulse falls obliquely on the plate it is no longer possible to consider 
the plate as though it were moving aS a whole. The pressure pulse will in fact travel along the 
plate and give rise to a corresponding disturbance in the plate and it is possible to consider a 
variety of possible conditions of support which would give rise to corresponding motions. The 
simplest of these and the most closely analogous to the case of normal incidence already discussed 
is to assume that the plate has no stiffness in bending and that it is supported in such a way that 
each element of it can vibrate freely in a direction normal to its plane with frequency u/2 7. 
It is shown in the first part of this report tnat the pressure on an oblique fixed and rigid plane 
only develops its final value (twice that in tne incident pulse) at some distance from the leading 
edge where the pulse first strikes it. It would be difficult-to take account of the finite mass 
of the plate as well as the distance from the leading edye; accordingly only the motion of the 
plate far from the leading edge will be considered. In this case the pressures in the incident 
and reflected pulses may be assumed in the forms 
=n (ope te 
Pj = Py (14) 
p= p.@(t+Xsing _ y cos@ y (15) 
r ° c Cc 
where @ is the angle of incidence and y is measured parallel to the plate. 
The pressure at x = 0 is therefore 
Bipampaaciebesd: 84 %eA 8 (et) oF (16) 
where t' = t — (y cos @)/c. (17) 
The equation of continuity at the surface is now 
sie = MM g(t") (18) 
° 
where € now represents d &/dt'. 
With the above mentioned assumption that the plate has no stiffness in bending, the equation of 
motion is identical with (6) and the equation for ¢ assumes the form 
msin@ msin@ 
d + RC ¢ + wd = Ls Seo are es ent! (19) 
which is identical with (7) except that msin@ is substituted for mand t' for t. 
The ceccse 
